WASHINGTON — As the debt ceiling debate enters its final stages, House Republicans face increasing political isolation in their opposition to sweeping budget reforms that President Barack Obama has pushed for and polls show most Americans now prefer.

Republican resistance to compromise has turned a significant block of voters against them, according to several new polls, and has frustrated members of their own leadership as well as establishment GOP figures.

The fear among leading Republicans is that the party may lose an opportunity to lock in budget cuts that go beyond anything that Democrats had previously been willing to consider. Five-term Rep. Tom Cole, R-Okla., said he has never seen spending reductions attached to a debt ceiling vote.

“It’s inconceivable,” Cole said. “Some of the members who haven’t been here don’t appreciate how much John Boehner has gotten for them.”

Boehner, the Ohio Republican and House speaker, now is leading an effort to try to prepare his restive House Republicans for a vote to raise the nation’s borrowing limit.

Republicans in the Senate have begun lining up behind a plan offered by a bipartisan group known as the “Gang of Six” to reduce the long-term deficit by nearly $4 trillion over the next decade. But that plan would include about $1.2 trillion in additional tax revenues over the 10-year period that House Republicans so far have resisted.

The White House indicated for the first time Wednesday that Obama would be willing to accept a short-term, stop-gap plan, but only for a few days, while Congress worked out the legislative details of a larger fix. Obama met with congressional leaders Wednesday, but no breakthrough was reported.

Either way, House Republicans remain the key obstacle to passing a debt ceiling increase and avoiding a possible federal default after Aug. 2. The party’s strict adherence to its no-new-taxes pledge all but rules out consideration of a larger agreement on deficits and the debt ceiling.

Their position is reinforced by the fear that tea party groups will mount primary challenges against many Republicans who vote for anything that could be characterized as a tax increase.

Rep. Michele Bachmann, R-Minn., and other high-profile conservatives have amplified such worries by harshly denouncing compromise proposals. Bachmann, who is seeking the GOP presidential nomination, began airing a new television ad in Iowa Wednesday reiterating her opposition to a debt limit increase.

Many House GOP members came into office with expectations that their new movement would quickly succeed in shrinking the government and halting the growth of debt — expectations many GOP leadership figures consider unrealistically high.

Boehner, at the center of negotiations with the White House over a sweeping deficit-reduction deal, also has had to spend much of the last several days trying to get his members to lower their expectations and ease their hostility to a compromise.

On Tuesday, he arranged a vote designed to appeal to conservatives by linking a debt ceiling increase to tight spending caps. The vote passed the House, but is considered unlikely to advance. Still, by doing so, Boehner gave conservatives a showcase vote while also nudging them off their rigid opposition to lifting the debt ceiling. That step could make it easier to approve a new measure in the days ahead.

The Republican enthusiasm for budget cuts over compromise may leave Republicans with less they could have otherwise achieved. Obama had proposed a 3-to-1 ratio of spending cuts to tax increases, even carving into Medicare and Social Security while drawing opposition from within his own ranks.

Such a deal would substantially curtail the growth of government in ways many conservatives want.

The president’s approach has increasingly won over the vast majority of Americans who, according to a growing body of polling, blame Republicans for not acting in the country’s best interest. Voters do not support tax breaks for corporations and wealthy Americans that the GOP wants to preserve.