House Speaker John Boehner of Ohio, arrives at the U.S. Capitol in Washington, Saturday, Sept. Heat is building on balkanized Republicans, who are convening the House this weekend in hopes of preventing a government shutdown but remain under tea party pressure to battle on and use a must-do funding bill to derail all or part of President Barack Obama's health care law. AP Photo/Molly Riley House Majority Leader Eric Cantor of Va., walks out of a Republican caucus at the U.S. Capitol in Washington, Saturday, Sept. Lawmakers from both parties urged one another in a rare weekend session to give ground in their fight over preventing a federal shutdown, with the midnight Monday deadline fast approaching. House Speaker John Boehner of Ohio, walks out of a Republican caucus at the U.S. Capitol in Washington, Saturday, Sept. WASHINGTON (AP) - Locked in a deepening struggle with President Barack Obama, House Republicans demanded a one-year delay in major parts of the nation's new health care law and permanent repeal of a tax on medical devices Saturday as the price for preventing a partial government shutdown threatened for early Tuesday. Senate Democrats rejected the plan even before the House could post it online for the public, and Majority Leader Harry Reid noted that Obama already has threatened to veto anything that delays or defunds the health law a few days from taking full effect. Undeterred, House Republicans pledged to press ahead with their latest attempt to squeeze a concession from the White House in exchange for letting the government open for business normally on Tuesday. They also agreed to pass legislation assuring U.S. troops are paid in the event of a shutdown. "I think we have a winning program here," said Rep. Hal Rogers, R-Ky., chairman of the House Appropriations Committee, after days of discord that pitted Speaker John Boehner, R-Ohio, and his leadership against tea party-backed conservatives. There was no immediate reaction from the White House. Obama said Friday he would not be party to eviscerating the law he won from Congress in his first term, and spokesman Jay Carney said the administration would "absolutely not" back repealing the medical devices tax. 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. The Senate rejected that measure 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 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 Senate Majority Leader Harry Reid of Nevada 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, Rep. Mo Brooks, R-Ala., said, "It depends on how long ... Reid wants to continue to be financially irresponsible and obstructionist. Said Rep. Charles Dent, R-Pa.: "Once this passes the House, the Senate's going to have to make a decision. Will they move quickly or will they dawdle? 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. There was little doubt that Reid had the votes to block a one-year delay in the health care program widely known as "Obamacare." 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, and that several members of Obama's party supported the proposal. In fact, the total was more than half the Democratic senators, 33 in all. Those in favor included members of the leadership, Sens. Dick Durbin of Illinois and Chuck Schumer of New York among them, as well as Murray. "What will move this is if there are other Democratic senators who put pressure on Reid," said Rep. Richard Hudson, R-N.C. The 2.3 percent tax, which took effect in January, is imposed on items such as pacemakers and CT scan machines; eyeglasses, contact lenses, hearing aids and other items are exempt. Repealing it would cost the government an estimated $29 billion over the coming decade. Some Republicans breathed defiance, despite fears inside the party that the GOP would bear the blame for any interruption in government services. I've got a titanium backbone. Let 'em blame, let 'em talk, it's fine," said Rep. Marsha Blackburn, R-Tenn. She said the GOP wanted to keep the government open, but also wanted to reduce its size and "delay, defund, repeal and replace Obamacare," as the health law is called. Despite such claims, House Republicans have yet to offer a replacement measure for the law they have pledged to repeal. They first promised to do so three years ago, during the 2010 election campaign when they wrested a majority from the Democrats. 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 patrolling the borders, inspecting meat and controlling air traffic would continue. The new health insurance exchanges would 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. Associated Press writer Alan Fram contributed to this report.