"I think we have a winning program here," said Republican Rep. Hal Rogers, chairman of the House Appropriations Committee, after days of discord that pitted Speaker John Boehner and his leadership against the party's ultraconservative tea party wing.
Failure to pass a short-term measure to keep the government running would mean the first partial closing in almost 20 years. A single, agreed-upon version must be approved by both houses of Congress and signed by Obama by Tuesday.
Such paralyzing fiscal fights have dominated Washington in recent years, underscoring the deep divide between the Republicans and the Obama administration and its Democratic allies. The two sides have managed in the past to come up with last-minute compromises to avoid a government shutdown.
Apart from its impact on the health care law, the legislation that House Republicans decided to back would assure routine funding for government agencies through Dec. 15.
The measure marked something of a reduction in demands by House Republicans, who passed legislation several days ago that would permanently strip the health care law of money while providing funding for the government.
It also contained significant concessions from a party that long has criticized the health care law for imposing numerous government mandates on industry, in some cases far exceeding what Republicans were willing to support in the past.
Republican aides said that under the legislation headed toward a vote, portions of the health care law that already have gone into effect would remain unchanged. That includes requirements for insurance companies to guarantee coverage for pre-existing conditions and to require children to be covered on their parents' plans until age 26. It would not change a part of the law that reduces costs for seniors with high prescription drug expenses.
Instead, the measure would delay implementation of a requirement for all individuals to purchase heath care coverage or face a penalty, and of a separate feature of the law that will create marketplaces where individuals can shop for coverage from private insurers.
By repealing the medical device tax, the Republican measure also would raise deficits an irony for a party that won the House majority in 2010 by pledging to get the nation's finances under control.
The Senate rejected the most recent House-passed anti-shutdown bill on a party-line vote of 54-44 Friday, insisting on a straightforward continuation in government funding without health care-related add-ons.
That left the next step up to the House with time to avert a partial shutdown growing ever shorter.
For a moment at least, the revised House proposal papered over a simmering dispute between the leadership and tea party conservatives who have been more militant about abolishing the health law that all Republicans oppose.
It was unclear whether members of the rank and file had consulted with Texas Republican Sen. Ted Cruz, who has become the face of the "Defund Obamacare" campaign that tea party organizations are promoting and using as a fundraising tool.
Instead, House Republican moderates and conservatives said it soon would be up to Reid and fellow Democrats to decide whether the government would remain open past the shutdown deadline of midnight Monday.
Asked if the House measure would risk a shutdown, Republican Rep. Mo Brooks said, "It depends on how long ... Reid wants to continue to be financially irresponsible and obstructionist."
There was little doubt that Reid had the votes to block a one-year delay in the health care program widely known as "Obamacare."
In debate on the House floor, Republicans adamantly rejected charges that they seek a government shutdown, and said their goal is to spare the nation from the effects of a law they said would cost jobs and reduce the quality of care. The law is an "attack and an assault on the free enterprise and the free economy," said Rep. Pete Sessions.
Left unspoken was how the House would respond if the Senate rejected the measure and insisted once more on a bill with no extraneous items.
Some moderate Republicans fear that their party would bear the blame for any interruption in government services. Closing down the government could weaken Republicans heading into an even more important battle later in October over raising the debt ceiling to allow the government to borrow more money.
It appeared the Republicans' chances of winning a concession centered on the medical device tax, which was incorporated into the health law to help pay its costs. Some Republicans noted that the Senate has taken a nonbinding 79-20 vote to repeal the levy, with more than half of the Senate Democrats supporting the proposal.
The 2.3 percent tax, which took effect in January, is imposed on items such as pacemakers and CT scan machines. Repealing it would cost the government an estimated $29 billion over the coming decade.
If lawmakers miss the approaching deadline, a wide range of federal programs would be affected, from the national parks to the Pentagon.
Some critical services such as patrolling the borders, inspecting meat and controlling air traffic 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.
The new health care insurance exchanges set up under the health care law are due to open Tuesday, a development that's lent urgency to the drive to use a normally routine stopgap spending bill to gut implementation of the law.
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Associated Press writers David Espo and Alan Fram and radio reporter Gerry Bodlander contributed to this report.