Faced with criticism from within their party, House Republicans wrestled Monday night with the next step in their politically risky and increasingly isolated battle against a bipartisan deal to preserve a tax break for working Americans.

After calling lawmakers back to Washington, the Republican-led House first delayed and then canceled an evening vote on a Senate-brokered compromise to extend the payroll tax cut for two months. House Republicans said they remained opposed to a short-term deal but were rethinking strategy on how to achieve their preferred goal: a one-year tax cut paid for with spending cuts and new revenue.

The maneuvering underscored the political rabbit trick House Republicans are trying to pull off. They are nearly alone in Washington in their opposition to the short-term compromise, which passed the Senate with overwhelming Republican support and was intended to give lawmakers more time to negotiate a one-year extension. President Obama endorsed the stopgap measure as the best way to avoid a tax increase when the current one expires Dec. 31.

After passing the bill Saturday, the Senate left town for the holidays and is not scheduled to return until Jan. 23.

That has left the House and its cast of hard-charging conservatives looking for leverage and accusing the Senate of passing along bad policy. At a closed-door meeting late Monday, the Republican troops rallied around references to the film “Braveheart” as they dug in for a prolonged battle.

“Our members do not want to just punt and do a two-month short-term fix where we have to come back and do this again. We’re here. We’re willing to work,” said House Speaker John A. Boehner (R-Ohio).

Boehner had declared Monday morning that he expected the House to vote down the Senate deal and then vote to initiate new negotiations.

But as the day wore on, lawmakers appeared increasingly hesitant to be seen voting against the compromise. Late Monday night, leaders instead crafted a bill that would allow lawmakers to vote in favor of something — a measure disagreeing with the Senate deal and initiating a conference committee.

The pressure to pass the deal was mounting from Democrats and Republicans. Several Republican senators questioned the House GOP’s strategy.

Sen. Scott Brown (R-Mass.) called the House rejection of the Senate bill “irresponsible and wrong.” Sen. Richard G. Lugar (R-Ind.) said the Senate compromise was “best for the country.” Sen. Dean Heller (R-Nev.) said there was no reason to hold up the short-term extension. “What is playing out in Washington, D.C., this week is about political leverage, not about what’s good for the American people,” he said.

Their complaints were echoed by Senate Majority Leader Harry Reid of Nevada and the WhiteHouse. Neither indicated any willingness — or political motivation — to revive talks.

Middle-class tax cuts are popular with voters and economists, and Democrats think the issue favors them. They presented the Senate deal as the last ship sailing and geared up to blame Republicans for the looming tax hike, which would increase taxes an average of $1,000 annually for workers.

“If Republicans vote down the bipartisan compromise negotiated by Republican and Democratic leaders, and passed by 89 senators including 39 Republicans, their intransigence will mean that in 10 days, 160 million middle-class Americans will see a tax increase,” Reid said Monday.

This could not have been where Boehner aimed to land when he urged the Senate last week to pass its own bill and let Reid and Senate Minority Leader Mitch McConnell (R-Ky.) lead the talks. The move was a shift for Boehner, who had engaged with Reid and the president directly in last summer’s talks over raising the debt ceiling and cutting spending.

But the brokered agreements Boehner has brought to the House have encountered increasing opposition from his rank and file, particularly conservatives who show scant allegiance to the speaker and no patience for Washington deal-making. Boehner lost 101 of 242 Republican votes in a November vote on a spending bill, a surprise blow and an indication of his limited control.

Now Boehner has come under criticism for failing, or being unable, to push his troops to support the compromise.

The White House tried to cast Boehner as reversing himself in an effort to cater to conservatives. “So he was for it before he was against it,” White House spokesman Jay Carney said Monday.

Boehner denied that account and said he raised concerns about settling for a short-term deal before it was done.

The president has delayed his Hawaiian vacation, and Carney suggested that Obama would stay in Washington if the impasse persisted.

While Democrats hammered Republicans for potentially allowing a tax increase, Republicans argued that they were the lone defenders of good policy and work ethic in Washington — and their criticism included their Republican colleagues.

Also Monday, a national payroll consortium warned that companies might find applying the stopgap measure unworkable because of technical difficulties, a prospect the GOP seized on to make its case for the broader one-year extension.

Rep. Tom Reed (R-N.Y.) said he was “very troubled” by the Senate Republicans agreeing to the deal.

“I will freely admit I do not understand why my Republican colleagues in the Senate went along with this,” said Rep. Bill Huizenga (R-Mich.), who said he was fired up for the fight.

“Maybe this is the beauty of being a freshman. You don’t know what you’re up against when it comes to old Washington and their expectations,” he said. “I’m sorry we’re going to be the skunk at the garden party with a bunch of people who want to go home for Christmas.”

kathleen.hennessey@latimes.com

lisa.mascaro@latimes.com

Times staff writer Peter Nicholas in Honolulu contributed to this report.