A threatened government shutdown only hours away, House Republicans scaled back their demands for delays in the nation’s health care overhaul Monday night as the price for essential federal funding. But President Barack Obama and Democrats rejected the proposals as quickly as they were made.

“We’re at the brink,” said Sen. Barbara Mikulski, D-Md.

On a long day and night in the Capitol, the Senate torpedoed one GOP attempt to tie government financing to changes in “Obamacare,” and House Republicans countered with a second despite unmistakable signs their unity was fraying.

The stock market dropped on fears that political gridlock between the White House and a tea party-heavy Republican Party would prevail, though analysts suggested significant damage to the national economy was unlikely unless a shutdown lasted more than a few days.

Still, a shutdown would send hundreds of thousands of workers home and inconvenience millions of people who rely on federal services or are drawn to the nation’s parks and other attractions. Some critical parts of the government — from the military to air traffic controllers — would remain open.

As lawmakers squabbled, President Barack Obama urged House Republicans to abandon demands he said were designed to “save face after making some impossible promises to the extreme right of their party.” Speaking of the health care law that undergoes a major expansion on Tuesday, he said emphatically, “That funding is already in place. You can’t shut it down.”

House Speaker John Boehner responded a few hours later on the House floor. “The American people don’t want a shutdown and neither do I,” he said. Yet, he added, the new health care law “is having a devastating impact. … Something has to be done.”

For all the Republican defiance, it appeared that Senate Majority Leader Harry Reid and fellow Democrats had the upper hand in the fast-approaching end game, and that Republicans might soon have to decide whether to allow the government to remain open — or come away empty-handed from a bruising struggle with Obama.

Some Republicans balked, moderates and conservatives alike.

Rep. Phil Gingrey of Georgia said it felt as if Republicans were retreating, given their diminishing demands, and Rep. Scott Rigell of Virginia said there was not unanimity when the rank and file met to discuss a next move.

Yet for the first time since the showdown began more than a week ago, there was also public dissent from the Republican strategy that has been carried out at the insistence of tea party-aligned lawmakers working in tandem with GOP Sen. Ted Cruz of Texas.

Rep. Charles Dent, R-Pa., said he was willing to vote for stand-alone legislation that would keep the government running and contained no health care-related provisions. “I would be supportive of it, and I believe the votes are there in the House to pass it at that point,” the fifth-term congressman said.

Other Republicans sought to blame Democrats for any shutdown, but Dent conceded that Republicans would bear the blame, whether or not they deserved it.

Hours before the possible shutdown, the Senate voted 54-46 to reject the House-passed measure that would have kept the government open but would have delayed implementation of the health care law for a year and permanently repealed a medical device tax that helps finance it.

In response, House Republicans sought different concessions in exchange for allowing the government to remain open. They called for a one-year delay in a requirement in the health care law for individuals to purchase coverage. The same measure also would require members of Congress and their aides as well as the president, vice president and the administration’s political appointees to bear the full cost of their own coverage by barring the government from making the customary employer contribution.

“This is a matter of funding the government and providing fairness to the American people,” said Boehner. “Why wouldn’t members of Congress vote for it?”

Unimpressed, the White House issued a veto threat against the bill and Democrats said they would sweep it aside in the Senate.

Obama followed up his public remarks with phone calls to Boehner and the three other top leaders of Congress, telling Republicans he would continue to oppose attempts to delay or cut federal financing of the health care law.

Boehner spokesman Brendan Buck said the House’s top Republican told the president that the health care law was costing jobs and that it was unfair that businesses were getting exemptions but American families were not.

The impact of a shutdown would be felt unevenly.

Many low-to-moderate-income borrowers and first-time homebuyers seeking government-backed mortgages could face delays, and Obama said veterans’ centers would be closed.

About 800,000 federal workers, many already reeling from the effect of automatic budget cuts, would be ordered to report to work Tuesday for about four hours — but only to carry out shutdown-related chores such as changing office voicemail messages and completing time cards.

Some critical services such as patrolling the borders and inspecting meat would continue. Social Security benefits would be sent, and the Medicare and Medicaid health care programs for the elderly and poor would continue to pay doctors and hospitals.

U.S. troops were shielded from any damage to their wallets when the Senate approved legislation assuring the military would be paid in the in the event of a shutdown. The House passed the bill early Sunday morning.

That had no impact on those who labor at other agencies.

“I know some other employees, if you don’t have money saved, it’s going to be difficult,” said Thelma Manley, who has spent seven years as a staff assistant with the Internal Revenue Service during a 30-year career in government.

As for herself, she said, “I’m a Christian, I trust in God wholeheartedly and my needs will be met.” She added, “I do have savings, so I can go to the reserve, so to speak.”

The last time the government shut down, in 1996, Republicans suffered significant political damage, and then-President Bill Clinton’s political fortunes were revived in the process.

Now, as then, Republicans control the House, and senior lawmakers insist even a shutdown isn’t likely to threaten their majority in the 2014 elections. “We may even gain seats,” Oregon Rep. Greg Walden, who chairs the party campaign committee, said recently.

For all the controversy about other matters, the legislation in question is a spending bill — and there was little if any disagreement about the spending-related issues.

The House and Senate have agreed to fix spending for a wide swath of federal programs at an annual level of $986 billion for the budget year that begins Oct. 1, the same as for the 12 months just ending.

Without separate legislation to make further reductions, across-the-board cuts would automatically take effect early next year that would reduce the level to $967 billion.

(AP)