WASHINGTON - Republican leaders in the House may have avoided steering their entire party toward political disaster in 2012 by giving up Thursday on their refusal to back a short-term extension of a payroll-tax cut.

But their weeklong obstinacy may have given President Obama an important boost.

The GOP change of heart came after days of relentless pressure from the White House and friendly fire from many conservatives. The political fallout is likely to linger.

"This just reinforces the public's suspicions about the Republican Party, which were already pretty negative," said Michael Dimock, associate director of the nonpartisan Pew Research Center.

Until Speaker John A. Boehner (R., Ohio), capitulated, House Republicans had seemed to be playing into Obama's hands. It was reminiscent of 1995-96, when Newt Gingrich led the House GOP and Democrat Bill Clinton was president. Gingrich overplayed his hand in a fight over budget priorities, Clinton refused to go along, and the federal government shut down twice - the second time from Dec. 15 to Jan. 6. Clinton persuaded the public that GOP extremism was to blame and coasted to an easy reelection that fall.

Like Clinton in 1995, Obama has been positioning himself since Labor Day as the protector of the middle class. He has called almost daily for a tax hike on millionaires to underscore his distinction from Republicans.

Obama has already gained in polls. A survey for CNN taken Dec. 16 to 18 put his approval rating at 49 percent, up 5 points from last month. And an ABC News-Washington Post poll released this week showed that 50 percent of Americans trust Obama more to protect the middle class, versus 35 percent who trust Republicans. Last month, they had been more evenly matched.

Obama "has the high ground," said Bruce Buchanan, a professor of government at the University of Texas, though he warned, "Events can change that."

The 1995-96 budget debate was an inside-the-Beltway phenomenon in holiday season, too - until it forced real consequences on the country by shutting down the government. Similarly, the current fight could be forgotten unless the two sides deadlock again in two months and taxes go up.

If that happens, it is the president who possesses "the bully pulpit" to shape public perception of who's to blame.

"Incumbent presidents have enormous advantages," Newt Gingrich observed Wednesday, recalling how Clinton triumphed over him in 1996. "It's very hard for the legislative branch to outperform the president in communications. . . . He has all the advantages of the White House as a backdrop, and my experience is, presidents routinely win."

The memory of House GOP brinksmanship could persist in voters' minds, a vivid reminder of partisan and ideological logjams that have plagued Congress all year, since Republicans recaptured control of the House. Their insistence on no-compromise budget stands almost shut the government in April and led to the summer's debt-ceiling debacle that saw U.S. debt's trustworthiness downgraded.

Then, last month, the bipartisan supercommittee charged with finding a budget compromise collapsed in failure. Through it all, polls made clear that the public is disgusted and increasingly blames Republicans more than Democrats.

Where Obama could benefit, analysts said, is that it reinforces his message that Republicans in Congress are obstructionist.

However, analysts cautioned, Obama's fate ultimately will rest on the performance of the economy and the identity of his still-to-be-determined GOP opponent.

"Relative to Congress, he looks great," said Dimock. "But that's all going to change once they choose a nominee."