House Speaker John A. Boehner (R-Ohio), flanked by House Republicans. (Alex Wong/GETTY IMAGES)

House Republicans faced mounting pressure Wednesday from critics inside and outside Congress who worry that their standoff with President Obama over whether to extend a payroll tax cut could do lasting damage to the GOP.

Former House speaker Newt Gingrich, who is seeking the party’s presidential nomination, warned that the showdown could end badly for Republicans, citing his own experience in losing the political battle to President Bill Clinton during the 1996 government shutdown.

“Incumbent presidents have enormous advantages. And I think what Republicans ought to do is what’s right for America. They ought to do it calmly and pleasantly and happily,” Gingrich said.

The Wall Street Journal’s editorial board captured the frustration among Republicans in the paper’s Wednesday editions, asking whether the GOP’s handling of the tax debate “might end up re-electing the President before the 2012 campaign even begins in earnest.”

Sen. Bob Corker (R-Tenn.) said the House GOP must get past the issue.

“Are Republicans getting killed now in public opinion? There’s no question,” he said Wednesday on CNBC. “Both Republicans and Democrats have agreed that this is going to happen, and probably the best thing to happen now is just to get it over with.”

In private, the criticism is more stark. Interviews with nearly 10 current and former congressional Republican advisers produced a range of deep criticism.

The most recurring critique was that Senate Minority Leader Mitch McConnell (R-Ky.) left a Friday meeting with House Speaker John A. Boehner (R-Ohio) and House Majority Leader Eric Cantor (R-Va.) expecting enough House support to approve the plan, allowing even some of the staunchest conservatives in the Senate to support the legislation.

“If they insisted on going down this terrible political path, then at a minimum they all needed to stay here then, pounding the drum and demanding the Senate Democrats get back to work. They could at least own the microphones and put Obama in a bad situation with his desire to go to Hawaii,” said a Senate Republican strategist who spoke on the condition of anonymity to freely criticize the House speaker.

A former aide to House GOP leaders suggested that, at least while the lawmakers are home, they might hear from real people who are concerned about losing their tax and unemployment benefits.

“Now they have an opportunity to hear from local media and constituents in their districts who are probably hammering them. If they were stuck in Washington, they’d have limited exposure,” he said. He suggested that they “get this issue out of the way before New Year’s, even if they take the political beating for it inside the Beltway.”

The friendly-fire attacks have threatened to undermine House leaders’ position that they did the right thing in rejecting a bipartisan Senate deal to extend the federal payroll tax for two months. The Senate approved the deal on Saturday with an overwhelming 89 votes, including 39 from Republicans. The House rejected it Tuesday, arguing that it was an unacceptable short-term fix and demanding that Senate Democrats reopen negotiation on a full-year extension of the tax cut.

The standoff has put Republicans in the unusual place of having to play defense on lower taxes, a conservative cause for three decades that is being turned against them.

Obama called Boehner on Wednesday to urge him again to allow a vote on the Senate-passed measure, which also would extend unemployment benefits and avert a cut in the reimbursement rate for doctors who treat Medicare patients. If the payroll tax holiday is not renewed, about 160 million Americans would feel it in their pocketbooks next year; the average worker would pay about $1,000 more over the course of the year.

Boehner showed no signs of caving to the pressure, either from Obama or his own allies. He held a meeting Wednesday morning with eight Republicans he chose to negotiate with the Senate and brushed off the criticism, saying his party will retain its advantage on the tax issue.

“We are the party of lower taxes for the American people. We have fought for lower taxes for the 21 years that I’ve been in this Congress, and we’re going to continue to be the party of lower taxes,” Boehner told reporters at the outset of his meeting with Republican lawmakers.

Obama has made extending that benefit for another year his top priority in a jobs agenda that has otherwise floundered on Capitol Hill. Most Republican leaders have agreed to support the measure as long as offset cuts in spending are made so the package would not add to the federal deficit. Many of Boehner’s rank-and-file members, however, question the effectiveness of the plan and are demanding additional concessions, such as forcing Obama to make a speedy decision on the construction of an oil pipeline.

In negotiations with Senate Majority Leader Harry M. Reid (D-Nev.), McConnell won the inclusion of the pipeline legislation, but the two leaders agreed on only $36 billion in spending cuts, which would cover just a two-month extension of the expiring provisions.

Hours after 39 Senate Republicans joined 50 other senators in supporting the compromise, House Republicans exploded on a Saturday conference call in opposition to the two-month plan.

“Nobody in their right mind thinks that two months is better than a year’s extension, and we’re determined to make that happen,” freshman Rep. Nan A.S. Hayworth (N.Y.) said Wednesday at the meeting with Boehner.

The House and the Senate are formally shuttered this week, opening only for brief pro forma sessions at which no legislative business will be performed. Reid has said that he will not open the Senate and that the House should instead just pass the Reid-McConnell plan and resume negotiations for a longer-term plan next month.

The White House has set up a countdown clock on its Web site, saying that the average worker will lose $20 a week if the tax cut is not extended. It singles out the House as the lone obstacle.

A growing number of Senate Republicans, having approved the short-term extension Saturday, have called on House Republicans to avoid any threat of a tax increase in the new year. About 10 GOP senators have said the best option would be to approve the short-term plan to avert the pinch in workers’ paychecks and to move off of an issue that has been politically damaging to the party.

On Tuesday night, Sen. John McCain (Ariz.), the 2008 Republican presidential nominee, said that the standoff is “harming” the party and that, in the near term, the House must relent.

“I think we have to recognize reality,” McCain told CNN. “And that is we are not going to see the payroll tax cut expire on the first of January. And we have to accommodate to that reality. It would not be fair to the American people at this time.”

Boehner found sympathy but no strong defense of his position among the party’s current presidential field.

“I’m not going to get into the back-and-forth on the congressional sausage-making process,” GOP presidential candidate Mitt Romney said. “I hope they’re able to sit down and work out a solution that works for the American people.”

Gingrich, who remains on friendly terms with Boehner, defended Boehner and said that he supports a one-year extension. A spokesman, however, declined to indicate the former speaker’s position on the short-term alternative.

Staff writers Dan Balz, Rosalind S. Helderman, Felicia Sonmez and Philip Rucker contributed to this report.