Senate Democrats, though, offered a less optimistic take late Saturday after Reid and other Democratic Senate leaders talked strategy at the White House with President Barack Obama for more than an hour. They were joined by Obama's chief of staff, Denis McDonough, deputy chief of staff Rob Nabors and Office of Management and Budget Director Sylvia Mathews Burwell.
A Senate Democratic leadership aide said the senators and the White House reviewed a number of options, but concluded that "while Democrats remain united, Republicans have yet to coalesce behind a clear negotiating position." The aide said Obama and the senators agreed that talks between Senate Democrats and Republicans should continue, but said the Democratic position remains the same: "Democrats are willing to negotiate on anything Republicans want to discuss, as soon as we reopen the government and pay our bills."
The government is expected to reach its debt limit Thursday, and parts of the government have been closed since Oct. 1.
While Reid and McConnell were polite and guardedly hopeful, most of those at the Capitol were glum. The momentum that had been building all week fizzled, and the day was marked by round after round of public finger-pointing and posturing.
The gloom was triggered Friday, when Obama essentially rejected a House Republican debt limit plan. Saturday, angry House Republican leaders gave colleagues a somber assessment of where things stand. They said they were now awaiting the president's next move and that no further talks were scheduled.
At the same hour, Reid and other senators were meeting, and afterward Reid said, "This should be seen as something very positive, even though we don't have anything done yet."
It was not clear where McConnell and Reid, two long-time legislative combatants, could find common ground. Democrats have insisted the government reopen before they negotiate on the budget. Republicans are reluctant to agree to a higher debt limit unless there are significant spending cuts.
Senators believe that the differences have narrowed to the point where disagreements can be broadly listed on a sheet of paper, meaning compromise is possible.
"There is a reason to believe that ultimately we will work it out," said Senate Assistant Majority Leader Richard Durbin, D-Ill.
Publicly, the sniping escalated Saturday. The Senate took a test vote on moving ahead with a Democratic plan to extend the debt limit through the end of next year. Republicans blocked the maneuver, essentially killing the measure.
House Republicans expressed doubts about Senate Republican ideas. House Democrats mounted a public effort to force a vote on reopening the government, angering Republicans. The White House was largely silent.
"Congress must do its job and raise the debt limit to pay the bills we have incurred and avoid default. It is unfortunate that the common sense, clean debt limit increase proposed by Senate Democrats was refused a yes or no vote today," said White House Press Secretary Jay Carney.
"Congress needs to move forward with a solution that reopens the government and allows us to pay our bills so we can move on to the business of achieving a broader budget deal that creates jobs, grows the economy and strengthens the middle class."