For weeks, the debt-ceiling debate has been defined by a clash of the extremes; tea party conservatives seeking to dramatically reshape government and committed liberals afraid that doing so would squeeze the poor and the working class.

But, in the end, it was largely a coalition of lawmakers in the middle — 174 Republicans, 95 Democrats — that pushed through a deal that is expected to avert a government default and allow the nation’s legal borrowing limit to rise through 2012.

With many of the conservatives who helped define the terms of the debate unwilling to vote for the deal that resulted, the bill’s fate instead was left to lawmakers such as Rep. Heath Shuler (N.C.), who belongs to a caucus of 25 conservative House Democrats known as the Blue Dogs.

There used to be 54 members in the caucus — until last year, when voters tossed nearly two dozen from office.

“Both parties are going to have the outer edges, the fringes within the party, they’ll vote against it. And the moderates will stand and vote for it,” Shuler said. “As always, the Blue Dogs are the ones who end up saving the day.” A similar coalition will be required in the Senate to pass the bill Tuesday and send it to the president for his signature.

On the other side of the aisle, Rep. Charlie Dent (Pa.), active in a group of moderate Republicans, said he felt an obligation to back the deal, and some irritation with colleagues who refused.

“I’ve expressed some frustration and anger to some of my colleagues here,” he said. “I heard too much from some of my colleagues about what they could never do,” he said, instead of what they could.

It was the most conservative elements of the GOP that forced a showdown over the national debt ceiling, promising even before the 2010 election to use what had always before been a routine congressional exercise as leverage to force broad changes in spending.

But, after a bipartisan deal was reached Sunday night, many of those same Republicans said they could not support it.

Rep. Joe Walsh (Ill.), for instance, said he was pleased that Republicans had won so much in the deal: The agreement would include no tax increases and about $1 trillion in discretionary spending cuts over the next decade.

“Thank God for these troublesome Republicans that have been sent to Congress,” Walsh, a freshman allied with the tea party movement, said Monday. “We’ve changed the conversation.”

So would Walsh vote for the deal he had helped win?

“No,” he said.

Walsh, like others in the House, wanted deeper cuts and a balanced budget amendment to the Constitution. “We have to do something dramatic. And this isn’t it,” he said.

Vice President Biden spent about two-and-half hours Monday meeting with Democrats, soothing liberals who think that the White House conceded too much in the deal, which will result in deep spending cuts in future years but offers no guarantee of higher taxes on the wealthy, as Democrats had sought.

The “no” votes included Rep. Michele Bachmann (R-Minn.), a presidential candidate who had promised in Iowa television ads never to vote to raise the debt ceiling. Also opposed was Black Caucus Chairman Emanuel Cleaver II (D-Mo.), who called the deal a “sugar-coated Satan sandwich” that would hurt the poor.

Some who did support the deal were convinced it was a genuinely productive step, a way to take a bite out of the national debt while giving neither party a total victory on taxes and entitlements.

Others were convinced by a more basic calculation.

“Default is not an option for the American people,” Rep. Steny H. Hoyer (D-Md.) said on the House floor. “At the very least, this bill averts that outcome.”

They were also comforted by the political dynamics of the deal, which was foisted on members by leaders of both parties, making the vote an unlikely campaign issue for either side next year.

At least, for now.

Former congressman Tom Davis of Virginia noted that many moderate Republicans were attacked in party primaries for their approval of the Troubled Assets Relief Program in 2008, which was hatched by a Republican president.

Davis — who leads an organization of centrist Republicans — said he worried that history could repeat itself for those who voted Monday to raise the debt ceiling.

“This thing smells okay today,” Davis said. “But, the further out you get from it, the more it’s going to stink,” as the urgency of the debt crisis fades and conservative groups examine the details.

Still, Davis said dozens of moderates had to support the plan.

“That’s kind of their lot in life,” he said, “that they always are the grown-ups.”

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Staff writers Lori Montgomery, Paul Kane and Felicia Sonmez contributed to this report.