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Debate in the House was along predictable lines, and only nine Republicans opposed the bill and five Democrats supported it on final passage.

“Our bloated and obese federal budget needs a healthy and balanced diet, one that trims the fat of overspending and grows the muscle of our nation’s economy,” said Rep. Reid J. Ribble, Wisconsin Republican, during debate on the measure.

Mr. Ribble is one of 87 first-term House Republicans determined to reduce the size of government.

Democrats said the measure, with its combination of cuts and spending limits, would inflict damage on millions who rely on Social Security, Medicare and other programs. “The Republicans are trying to repeal the second half of the 20th century,” said Rep. Sander M. Levin, Michigan Democrat.

Mr. Boehner played a muted role in public during the day. He did not speak on the House floor on the legislation but issued a statement afterward saying it “provides President Obama with the debt limit increase he’s requested while making real spending cuts now and restraining future government spending and debt that are hurting job growth.”

He did not discuss what alternatives he had in mind, although the Senate’s top two leaders have been at work on one that would let the president raise the debt limit without prior approval by Congress.

The Gang of Six briefed other senators on the group’s plan after a seemingly quixotic quest that took months, drew disdain at times from the leaders of both parties and appeared near failure more than once.

It calls for deficit cuts of slightly less than $4 trillion over a decade and includes steps to slow the growth of Social Security payments; cut at least $500 billion from Medicare, Medicaid and other health programs; and wring billions in savings from programs across the face of government.

It envisions tax changes that would reduce existing breaks for a number of popular items while reducing the top income bracket from the current 35 percent to 29 percent or less.

The tax overhaul “must be estimated to provide $1 trillion in additional revenue to meet plan targets,” according to a summary that circulated in the Capitol.

Some Republicans noted a claim contained in the summary that congressional bookkeeping rules actually could consider the plan a tax cut of $1.5 trillion. That credits sponsors for retaining income tax cuts enacted at all income levels when George W. Bush was president.

The Gang of Six includes three Democrats: Sens. Kent Conrad of North Dakota, Mark Warner of Virginia and Richard J. Durbin of Illinois, a member of the leadership.

The three Republicans, all conservatives, are Sens. Mike Crapo of Idaho, Tom Coburn of Oklahoma and Saxby Chambliss of Georgia, who has a particularly close relationship with Mr. Boehner dating to their days together in the House.

In recommending higher government revenues, Republicans in the group challenged party orthodoxy that has held sway for two decades, ever since President George H.W. Bush memorably broke his “no new taxes” pledge to make a deficit reduction deal with congressional Democrats.

In the years since, refusal to raise taxes has become a virtually inviolable article of faith among Republicans, and used by them and their allies in countless political campaigns against Democrats.

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