The entrenched sides had kept at their ping-pong battle earlier, with the Senate rejecting House-passed measures as soon as someone could physically bring the bill to the other side of the Capitol.
House Republicans continued to tie ongoing government funds to a one-year delay of the Democrats' signature health-care law, while Senate Majority Leader Harry Reid said the government would not be held hostage by GOP members still trying to fight the three-year old reform.
"With a bully, you cannot let them slap you around," Reid said.
Earlier, President Barack Obama, preparing for a possible shutdown, ticked off a list of programs that could be halted and said he would not negotiate with Republicans who were willing to shutter the government to get 100 percent of what they wanted.
"One faction, one branch of government doesn't get to shut down the entire government just to fight the results of an election. Keeping the people's government running is not a concession to me," Obama said. "You don't get to extract a ransom for doing your job, for doing what you're supposed to be doing anyway or because there's a law there that you don't like."
Republican Sens. Mike Lee of Utah and Ted Cruz of Texas had led the charge to use a budget resolution as leverage to force the Democrats to halt funding for the Affordable Care Act, also known as Obamacare, or leave the government without money to operate past Tuesday. By Monday night, the House had offered several different versions of a temporary budget measure, all of which attacked parts of the health-care law.
"I think the Republicans have given them a lot of decent things to vote on," Hatch, R-Utah, said earlier. Later in a statement, Hatch took aim at the Democrats for causing the government closure. "The fact is that Senate Democrats failed to take common sense action to fund the government and change Obamacare to protect the American people."
Lee said he was too busy to comment when asked off the Senate floor.
Senate leaders balked at a last-ditch effort by House leaders to set up a committee between the two chambers to iron out the differences on the budget legislation, arguing that such a move would come too late to stop a shutdown.
The game of brinkmanship had many worried about what the impact of the government closure would have on the nation's still-fragile economy.
"It's just the absolute unknown," said Salt Lake Chamber President Lane Beattie. "How long will it last? What is the real impact to business? Whether I'm selling widgets on a retail basis or whether I'm selling gadgets internationally, everyone wants to know."
Even as the hours ticked by, though, there was little movement from the standoff.
"It's sad. I don't like it. I'm frustrated," Rep. Rob Bishop, R-Utah, said, emerging from a closed-door Republican member-only meeting.
"Harry [Reid] only has half of Congress. He can't just simply say, take what we do or leave it. He can't play that game."
Both Republicans and Democrats, though, were playing a blame game on Monday, trying to pin a potential shutdown on the other side. A new national poll, though, showed more Americans were likely to say the GOP was at fault than Democrats, 46 percent to 36 percent, according to the survey by CNN/ORC International.
Rep. Chris Stewart, R-Utah, said he supported the delay of the health-care law being tied to a government funding bill and said that no one was looking at what the polls say on who would be blamed if it doesn't work out.
"There's a lot of us who feel that this law is very, very detrimental to the American people and we're looking for every opportunity [we] can to delay it as long as possible," Stewart said.
There were cracks in the GOP unity, though, and some Republicans were upset by being pressured to the brink by Lee and Cruz and their tea-party supporters.
"I respect their advocacy and their views. I disagree with them," Sen. John McCain, R-Ariz., said in response to a question by The Salt Lake Tribune. "I've said it for months: We will not repeal Obamacare, and sooner or later we will resume the functions of government without the [effort to] repeal Obamacare."
Sen. Chuck Schumer, D-N.Y., took it a step further, castigating House Speaker John Boehner for allowing his conservative flank to call the shots.
"By going along with the hard right, Speaker Boehner is like the ancient Mayans, making sacrificial offerings to the right-wing gods by refusing to accept a clean [budget resolution]," Schumer said. "He's putting the economy, the paychecks of millions of Americans on the sacrificial altar as he shuts down the government."