The Republican leader, Sen. Mitch McConnell of Kentucky, said he was "hopeful and optimistic" of a deal, adding he hoped a compromise could be presented to rank-and-file lawmakers as early as Sunday, a little more than 24 hours before the year-end deadline.
Said Majority Leader Harry Reid: "I'm going to do everything I can" to prevent the tax increases and spending cuts that threaten to send the economy into recession. He cautioned, "Whatever we come up with is going to be imperfect."
Officials said there was a general understanding that any agreement would block scheduled income tax increases for middle class earners while letting rates rise at upper income levels.
Democrats said Obama was sticking to his campaign call for increases above $250,000 in annual income, even though in recent negotiations he said he could accept $400,000.
The two sides also confronted a divide over estate taxes.
Obama favors a higher tax than is currently in effect, but one senior Republican, Sen. Jon Kyl of Arizona, said he's "totally dead set" against it. Speaking of fellow GOP lawmakers, he said they harbor more opposition to an increase in the estate tax than to letting taxes on income and investments rise at upper levels.
Also likely to be included in the negotiations are taxes on dividends and capital gains, both of which are scheduled to rise with the new year. Also the alternative minimum tax, which, if left unchanged, could hit millions of middle- and upper-income taxpayers for the first time.
In addition, Obama and Democrats want to prevent the expiration of unemployment benefits for the long-term jobless, and there is widespread sentiment in both parties to shelter doctors from a cut in Medicare fees.
The White House has shown increased concern about a possible spike in milk prices if a farm bill is not passed in the next few days, although it is not clear whether that issue, too, might be included in the talks.
One Republican who was briefed on the White House meeting said Boehner made it clear he would leave in place spending cuts scheduled to take effect unless alternative savings were found to offset them. If he prevails, that would defer politically difficult decisions on government benefit programs like Medicare until 2013.
Success was far from guaranteed in an atmosphere of political mistrust even on a slimmed-down deal that postponed hard decisions about spending cuts into 2013 in a Capitol where lawmakers grumbled about the likelihood of spending the new year holiday working.
In a brief appearance in the White House briefing room, Obama referred to "dysfunction in Washington," and said the American public is "not going to have any patience for a politically self-inflicted wound to our economy. Not right now."
If there is no compromise, he said he expects Reid to put legislation on the floor to prevent tax increases on the middle class and extend unemployment benefits an implicit challenge to Republicans to dare to vote against what polls show is popular.
The guest list for the White House meeting included Reid, McConnell, Boehner and House Democratic leader Nancy Pelosi, D-Calif.
The same group last met more than a month ago and emerged expressing optimism they could strike a deal that avoided the fiscal cliff. At that point, Boehner had already said he was willing to let tax revenues rise as part of an agreement, and the president and his Democratic allies said they were ready to accept spending cuts.
Since then, though, talks between Obama and Boehner faltered, the speaker struggled to control his rebellious rank and file, and Reid and McConnell sparred almost daily in speeches on the Senate floor. Through it all, Wall Street has paid close attention, and in the moments before the meeting, stocks were trading lower for the fifth day in a row.
The core issue is the same as it has been for more than a year, Obama's demand for tax rates to rise on upper incomes while remaining at current levels for most Americans. He made the proposal central to his successful campaign for re-election, when he said incomes above $200,000 for individuals and $250,000 for couples should rise to 39.6 percent from the current 35 percent.
Boehner refused for weeks to accept any rate increases, and simultaneously accused Obama of skimping on the spending cuts he would support as part of a balanced deal to reduce deficits, remove the threat of spending cuts and prevent the across-the-board tax cuts.
Last week, the Ohio Republican pivoted and presented a Plan B measure that would have let rates rise on million-dollar earners. That was well above Obama's latest offer, which called for a $400,000 threshold, but more than the speaker's rank and file were willing to accept.
Facing defeat, Boehner scrapped plans for a vote, leaving the economy on track for the cliff that political leaders in both parties had said they could avoid. In the aftermath, Democrats said they doubted any compromise was possible until Boehner has been elected to a second term as speaker when the new Congress convenes on Jan. 3.
Further compounding the year-end maneuvering, there are warnings that the price of milk could virtually double beginning next year.
Congressional officials said that under current law, the federal government is obligated to maintain prices so that fluid milk sells for about $20 per hundredweight. If the law lapses, the Department of Agriculture would be required to maintain a price closer to $36 of $38 per hundredweight, they said. It is unclear when price increases might be felt by consumers. Over the fiscal cliff: Soft or hard landing
Efforts to save the nation from going over a year-end "fiscal cliff" were still in disarray as lawmakers returned to the Capitol to confront the tax-and-spend crisis. A tone-setting quotation was Democratic Sen. Harry Reid's assertion that the House under Republican Speaker John Boehner had been "operating with a dictatorship."
President Barack Obama flew back to Washington from Hawaii after telephoning congressional leaders from his Christmas vacation perch. Once back, he set up a meeting with leaders of both parties at the White House late Friday to make a fresh attempt to find a solution before Monday night's deadline.
A look at why it's so hard for Republicans and Democrats to compromise on urgent matters of taxes and spending, and what happens if they fail to meet their deadline:
NEW YEAR'S HEADACHE
Partly by fate, partly by design, some scary fiscal forces come together at the start of 2013 unless Congress and Obama act to stop them. They include:
Some $536 billion in tax increases, touching nearly all Americans, because various federal tax cuts and breaks expire at year's end.
About $110 billion in spending cuts divided equally between the military and most other federal departments. That's about 8 percent of their annual budgets, 9 percent for the Pentagon.
Hitting the national economy with that double whammy of tax increases and spending cuts is what's called going over the "fiscal cliff." If allowed to unfold over 2013, it would lead to recession, a big jump in unemployment and financial market turmoil, economists predict.
WHAT IF THEY MISS THE DEADLINE?
If New Year's Day arrives without a deal, the nation shouldn't plunge onto the shoals of recession immediately. There still might be time to engineer a soft landing.
So long as lawmakers and the president appear to be working toward agreement, the tax hikes and spending cuts could mostly be held at bay for a few weeks. Then they could be repealed retroactively once a deal was reached.
The big wild card is the stock market and the nation's financial confidence: Would traders start to panic if Washington appeared unable to reach accord? Would worried consumers and businesses sharply reduce their spending? In what could be a preview, stock prices around the world dropped Friday after House Republican leaders' plan for addressing the fiscal cliff collapsed.
Federal Reserve Chairman Ben Bernanke has warned lawmakers that the economy is already suffering from the uncertainty and they shouldn't risk making it worse by blowing past their deadline.
WHAT IF THEY NEVER AGREE?
If negotiations between Obama and Congress collapse completely, 2013 looks like a rocky year.
Taxes would jump $2,400 on average for families with incomes of $50,000 to $75,000, according to a study by the non-partisan Tax Policy Center. Because consumers would get less of their paychecks to spend, businesses and jobs would suffer.
At the same time, Americans would feel cuts in government services; some federal workers would be furloughed or laid off, and companies would lose government business. The nation would lose up to 3.4 million jobs, the Congressional Budget Office predicts.
"The consequences of that would be felt by everybody," Bernanke says.
Much of the disagreement surrounds the George W. Bush-era income tax cuts, and whether those rates should be allowed to rise for the nation's wealthiest taxpayers. Both political parties say they want to protect the middle class from tax increases.
Several tax breaks begun in 2009 to stimulate the economy by aiding low- and middle-income families are also set to expire Jan. 1. The alternative minimum tax would expand to catch 28 million more taxpayers, with an average increase of $3,700 a year. Taxes on investments would rise, too. More deaths would be covered by the federal estate tax, and the rate climbs from 35 percent to 55 percent. Some corporate tax breaks would end.
The temporary Social Security payroll tax cut also is due to expire. That tax break for most Americans seems likely to end even if a fiscal cliff deal is reached, now that Obama has backed down from his call to prolong it as an economic stimulus.
If the nation goes over the fiscal cliff, budget cuts of 8 percent or 9 percent would hit most of the federal government, touching all sorts of things from agriculture to law enforcement and the military to weather forecasting. A few areas, such as Social Security benefits, Veterans Affairs and some programs for the poor, are exempt.
THERE'S MORE AT STAKE
All sorts of stuff could get wrapped up in the fiscal cliff deal-making. A sampling:
Some 2 million jobless Americans may lose their federal unemployment aid. Obama wants to continue the benefits extension as part of the deal; Republicans say it's too costly.
Social Security recipients might see their checks grow more slowly. As part of a possible deal, Obama and Republican leaders want to change the way cost-of-living adjustments are calculated, which would mean smaller checks over the years for retirees who get Social Security, veterans' benefits or government pensions.
The price of milk could double. If Congress doesn't provide a fix for expiring dairy price supports before Jan. 1, milk-drinking families could feel the pinch. One scenario is to attach a farm bill extension to the fiscal cliff legislation if a compromise is reached in time.
Millions of taxpayers who want to file their 2012 returns before mid-March will be held up while they wait to see if Congress comes through with a deal to stop the alternative minimum tax from hitting more people.
CALL THE WHOLE THING OFF?
In theory, Congress and Obama could just say no to the fiscal cliff, by extending all the tax cuts and overturning the automatic spending reductions in current law. But both Republicans and Democrats agree it's time to take steps to put the nation on a path away from a future of crippling debt.
Indeed, the automatic spending cuts set for January were created as a last-ditch effort to force Congress to deal with the debt problem.
If Washington bypassed the fiscal cliff, the next crisis would be just around the corner, in late February or early March, when the government reaches a $16.4 trillion ceiling on the amount of money it can borrow.
Boehner says Republicans won't go along with raising the limit on government borrowing unless the increase is matched by spending cuts to help attack the long-term debt problem. Failing to raise the debt ceiling could lead to a first-ever U.S. default that would roil the financial markets and shake worldwide confidence in the United States.
To avoid that scenario, Obama and Boehner are trying to wrap a debt limit agreement into the fiscal cliff negotiations.
SO WHAT'S THE HOLDUP?
They're at loggerheads over some big questions.
Obama says any deal must include higher taxes for the wealthiest Americans. Many House Republicans oppose raising anyone's tax rates. Boehner tried to get the House to vote for higher taxes only on incomes above $1 million but dropped the effort when it became clear he didn't have the votes.
Republicans also insist on deeper spending cuts than Democrats want to make. And they want to bring the nation's long-term debt under control by significantly curtailing the growth of Medicare, Medicaid and Social Security changes that many Democrats oppose.
Obama, meanwhile, wants more temporary economic "stimulus" spending to help speed up a sluggish recovery. Republicans say the nation can't afford it.
IT'S NOT JUST WASHINGTON
Seems like they could just make nice, shake hands and split their differences, right?
But there's a reason neither side wants to give ground. The two parties represent a divided and inconsistent America. True, Obama just won re-election. But voters also chose a Republican majority in the House.
Republican and Democrats alike say they are doing what the voters back home want.
Neither side has a clear advantage in public opinion. In an Associated Press-GfK poll, 43 percent said they trust the Democrats more to manage the federal budget deficit and 40 percent preferred the Republicans. There's a similar split on who's more trusted with taxes.
About half of Americans support higher taxes for the wealthy, the poll says, and about 10 percent want tax increases all around. Still, almost half say cutting government services, not raising taxes, should be the main focus of lawmakers as they try to balance the budget.
When asked about specific budget cuts being discussed in Washington, few Americans express support for them.
Time for deal-making is short, thanks to the holiday and congressional calendars. Some key dates for averting the fiscal cliff:
Lawmakers didn't begin returning to the Capitol until Thursday, leaving less than a week to vote on a compromise before year's end.
Obama returned Thursday from his Christmas vacation in Hawaii. The president asked congressional leaders to the White House Friday to try to resolve the fiscal cliff.
If lawmakers reach Dec. 31 without a deal, some economists worry that the financial markets might swoon.
The current Congress is in session only through noon Eastern time on Jan. 3. After that, a newly elected Congress with 13 new senators and 82 new House members would inherit the problem.
The Associated Press