In another test of House Speaker John A. Boehner’s leadership of his restive Republican majority, the House is expected to vote Tuesday on a GOP plan to extend a one-year reduction in the payroll taxes paid by 160 million workers.

Republicans have been divided over whether to extend the tax cut, as President Obama has urged, or allow the levy to revert to 6.2 percent in January from 4.2 percent.

That division was on display at Saturday’s Republican presidential debate, where three of the six candidates — including front-runners Newt Gingrich and Mitt Romney — urged Congress to extend the tax break, while three others argued that it wouldn’t spur job growth.

But by linking the tax cut with other Republican priorities — including speeding up construction of the controversial Keystone XL oil sands pipeline — and by paying for the package with other spending cuts, GOP leaders believe they’ve come up with a measure that can draw overwhelming Republican support.

House approval would set up a clash later this week with the Senate, where Democratic leaders have rejected key pieces of the House bill.

The showdown in the GOP-dominated House will be the highest-stakes vote for Boehner (Ohio) and his leadership team since September, when a stopgap government funding measure unexpectedly fell short of passage amid opposition from nearly all Democrats as well as 48 Republicans.

If most Democrats oppose the GOP payroll tax measure, as House Minority Leader Nancy Pelosi (D-Calif.) and others have suggested, Boehner can afford to lose the support of only about two dozen members of his 242-member conference when the bill comes to the floor.

Boehner is confident that the measure will pass. He cited an announcement by Rep. Dan Boren (D-Okla.) that he will vote “yes” on the House GOP plan and predicted that other Democrats would cross party lines as well.

“When it comes to jobs, the American people can’t wait. So we’re going to take action,” said Boehner, calling the pipeline project “as close to a shovel-ready project as you’re ever going to see.”

A Republican aide said conservative lawmakers have been persuaded to support the bill because of how its costs would be covered. The bill, which would also extend unemployment benefits and avert deep scheduled cuts in Medicare reimbursement rates for doctors for two years, would be paid for through spending cuts.

Those offsets include eliminating some funding for the federal health-care reform effort, extending a two-year pay freeze for government employees and reducing the federal workforce.

The payroll tax, which is split between workers and their employers, is used to fund Social Security benefits. Many Republicans, along with some Democrats, say repeated holidays in the tax rate could undermine the retirement program.

The bill includes other sweeteners for conservatives, including reforms to unemployment benefits that would reduce the maximum time emergency benefits could be extended from 99 weeks to 59 weeks. And the measure would delay Environmental Protection Agency regulations on industrial boiler emissions.

But Democrats continued to object to the GOP plan. White House press secretary Jay Carney argued that it was “essentially suggesting that there is a political trade-off to be had, that extending tax cuts for middle-class and working Americans should only occur in return for a political gift or an ideological item.”

A spokeswoman for the State Department, which is scheduled to rule on the pipeline project by early 2013, warned that the agency would be unable to complete necessary reviews in 60 days, as mandated by the House bill. If required to do so, she said, the department would be unable to recommend issuing a permit for its construction.

Twice, Democratic proposals to cut the payroll tax even further — dropping the rate to 3.1 percent — have failed to advance in the Senate because Democrats proposed paying for the cut with a new surtax on those making more than $1 million a year.

Senate Democrats are weighing the idea of introducing a proposal that would be funded entirely through spending cuts. Their latest suggestion might also use future savings from reducing overseas military commitments, which Boehner has rejected as an accounting gimmick.

House Republicans think passing their own measure Tuesday will give them an advantage as lawmakers prepare to leave town for the holidays.

“We’ll continue to have the upper hand in these negotiations until the Democratic leadership in the Senate is able to pass a bill,” a Republican aide said.

Staff writer David Nakamura contributed to this report.