Washington (CNN) -- Much of the government has been shutdown -- hundreds of thousands of workers furloughed, national parks closed, programs for anything from child care to space exploration shuttered -- for four days.
And it's likely to remain closed for several days if not weeks more, House Republicans concede.
Despite public pressure to reach a resolution -- and public promises they want to, if only the other side would give in -- Washington politicians remained at odds Friday. And there's little indication there will be any breakthrough until at least mid-October, when the next economic crisis comes up over whether Congress gives the federal government the OK to increase how much it can borrow, or else default on its debt.
"I don't see anything happening with the shutdown until we get some kind of a plan for a bigger agreement," Rep. Charles Boustany said after meeting Friday morning with fellow Republicans.
Among those at that closed-door meeting was House Speaker John Boehner. He spoke to reporters Friday as well, trying to ratchet up pressure on President Barack Obama to end the crisis following his approach -- negotiate changes to Obamacare as part of any deal.
Fuming about a Wall Street Journal report citing an unnamed Obama administration saying "we are winning," Boehner said, "This isn't some damn game!"
"The American people don't want their government shut down and neither do I," the Ohio Republican said. "All we are asking for is to sit down and to have a discussion and to bring fairness."
For his part, Obama said he and fellow Democrats are willing to negotiate with Republicans on budgetary matters -- but only after they agree to open up the government first.
"I'm happy to have negotiations," he said at a delicatessen near the White House. "We can't do it with a gun held to the head of the American people."
The president stressed that what's unfolding is very serious -- noting its impact on legions of government workers and contractors, not to mention those who rely on government's help.
"There is no winning when families don't have certainly about whether they're going to be paid or not," Obama said. "... As long as they're off the job, nobody's winning."
GOP legislator outlines possible solution
While the shutdown stalemate continues, some of the focus has shifted to the next potential crisis: what Congress does about the so-called debt ceiling, with experts warning of grave economic harm, both at home and abroad, if nothing is done.
The Treasury says the government is set to run out of money to cover its roughly $16.7 trillion debt on October 17, requiring an increase in the amount it can borrow.
Boehner told fellow GOP legislators this week that he won't allow the United States to default on its debt, even if it means getting help from Democrats to pass the necessary legislation, according to a Republican House member who requested anonymity to talk about the private meeting.
The speaker said publicly Friday that "I don't believe we should default on our debt," then repeated his longstanding contention that government spending must be cut so that the nation doesn't continue to rack up budget deficits.
Still, Democratic Sen. Charles Schumer of New York said the move could mark "the beginnings of a significant breakthrough."
"Even coming close to the edge of default is very dangerous, and putting this issue to rest significantly ahead of the default date would allow everyone in the country to breathe a huge sigh of relief," Schumer said.
Even with that deadline looming, top House GOP leaders didn't discuss plans to address the debt ceiling at the Friday morning meeting -- though smaller groups are looking into it. At a Thursday meeting, Boehner talked with a small group of Republicans to get a pulse on what the rest of the caucus wants.
"Boehner told us that we've got to get something with regard to (the) budget and the debt in order to raise the debt ceiling," one GOP member who attended the session told CNN.
Boustany, the Louisiana Republican, outlined what he thinks could serve as a framework for an agreement -- changes to entitlement programs that Obama has suggested before and detailed targets for tax reform, both items that Republicans want. In return, the GOP-led House could agree to raise the debt limit potentially through the rest of the president's term.
But the House Republican who met with Boehner said, given the calendar, there may not be enough time to enact substantial policy changes that Republicans and some Democrats would agree to.
"Everyone understands that the Obamacare issue may be out of reach, probably always was," the legislator said, referring to House GOP members' insistence that they wouldn't agree to a plan to fund the government unless it includes provisions to defund or delay parts of the 2010 Affordable Care Act.
"But if the president thinks he is going to be able to hold (his) ground with negotiations on the debt limit, he sounds like Ted Cruz," referring to the Texas senator and tea party favorite who has been one of the party's biggest, most steadfast thorns in Democrats' side.
Dems continue push for 'clean' spending bill
What Democrats have consistently said they want is for the House to pass a "clean" spending resolution without any Obamacare provisions, and like one that moved through the Democratic-led Senate.
Democratic Rep. Steve Israel of New York told CNN on Friday that at least 180 of the 200 House Democrats would vote for such a plan.
That means at least 37 Republicans out of the chamber's 233-strong majority would have to defy the party's strategy so far to reach the 217 threshold needed for the measure to pass and go to Obama's desk.
Israel said 20 House Republicans had publicly expressed support for such a move, and that he expected more than enough others to join them if the measure actually came up for a vote.
His fellow House Democrats said Friday they would try to get Republican colleagues to join them in a procedural move that would force a vote on a spending measure with no anti-Obamacare amendments. However, the earliest such a vote could occur under their tactic would be October 14, they said.
"This will at least start the clock ticking," said Democratic Rep. Chris Van Hollen of Maryland.
However, GOP Rep. Tim Huelskamp of Kansas described his caucus as "very unified" and said Democrats are "confused" if they think "we're going to fold and let them win on everything."
Obama and Democrats reject the GOP demands, calling them political extortion intended to force concessions on his signature piece of legislation that was upheld by the Supreme Court last year.
They say they already made a major concession to Republicans when Senate Democrats accepted a lower total funding figure in their proposed spending plan, which would cover the first 11 weeks of the new fiscal year that began Tuesday.
In the view of Democrats, Republicans forced the shutdown and now have no strategy for ending it without getting blamed.
"They're flopping around like dead fish in the bottom of the boat trying to figure out what to do next," Democratic Rep. Jim McDermott of Washington told CNN. "They have no plan B."
House takes piecemeal approach
Boehner and his GOP House leadership, meanwhile, say they will proceed with votes during a rare Saturday session on piecemeal spending legislation to fund popular programs.
House Republican leaders sought to frame the votes as forcing Democrats to go on the record for or against funding for things such as national parks and veterans affairs.
Other piecemeal spending measures would fund the Federal Emergency Management Agency and the National Weather Service, as well as the Head Start program, Majority Leader Eric Cantor of Virginia said Friday.
Democrats oppose the incremental approach, saying it amounts to conservatives choosing to fund programs and services they like.
And Obama would veto such measures if they reached his desk, the White House has said. On Friday, it said the president would sign a measure expected to pass Congress guaranteeing back pay for federal workers who are furloughed because of the shutdown.
The Pentagon may announce as soon as this weekend a plan to bring up to 400,000 furloughed civilian employees back to work, according to two Defense Department officials. CNN has learned the plan is in the final stages of being written and approved.
But even if that happens, another 400,000 government employees could still be furloughed. Others who are considered "essential" would work, albeit they won't get paid until the shutdown ends -- something that could take days, weeks or months more.
CNN's Deirdre Walsh and Tom Cohen reported from Washington, CNN's Greg Botelho wrote from Atlanta. CNN's Barbara Starr, Ed Payne, Jason Hanna and Josh Levs contributed to this report.