By Donna Smith

WASHINGTON (Reuters) - Republicans in the House of Representatives were falling into line on Thursday behind a bill to extend a payroll tax break for workers after leaders sweetened the legislation with a provision that has drawn a veto threat from President Barack Obama.

The move by House Republican leaders to link the popular tax cut to measures that are politically unpalatable to Obama and his fellow Democrats sets the stage for an end-of-the year partisan brawl that could feed growing voter disgust with Washington gridlock at a time of economic struggle.

The bill detailed by House Republican leaders in a closed door session includes a measure requiring quick approval of the Keystone XL pipeline that is to carry Canadian oil to Texas refineries. Obama has delayed approval of the project for a year to allow more review on its environmental impact.

A number of Republicans who had been reluctant to back the payroll tax cut say the House leaders had addressed their concerns and were now inclined to back the bill.

"Clearly, leadership listened to individuals," said Representative Phil Gingrey who told reporters he had switched from undecided last week to "I'm going to vote for this."

Obama said on Wednesday he would reject any payroll tax cut legislation that included the pipeline provision even though he and his fellow Democrats in Congress believe extending the tax cut for wage-earners is essential to help stimulate the sluggish U.S. economy.

The 4.2 percent payroll tax that workers pay to fund the Social Security retirement system will snap back to 6.2 percent in January if Congress fails to act.

The pipeline provision and the veto threat may have helped win conservative support for the payroll tax cut extension.

"It never hurts," Republican Representative Kevin Brady said when asked if Obama's veto threat helped galvanize reluctant conservatives.

Republicans had been sharply divided over the payroll tax cut, with conservatives questioning their leaders' support for continuing the lower rate.

The Republican-led House of Representatives is expected to vote on the legislation next week. The bill also includes an extension of unemployment insurance benefits coupled with reforms of the program and a measure to avert a pay cut for doctors treating patients on Medicare, the health program for the elderly.

DEMOCRATIC PLAN UNLIKELY TO PASS

The Democratic-controlled Senate is set to vote on Thursday afternoon on its version of the legislation. The Democratic proposal would cover the roughly $110 billion cost of extending the payroll tax cut with an extra tax on incomes over $1 million.

The measure is unlikely to overcome Republican procedural hurdles and lawmakers will have to strike some sort of compromise to pass the payroll tax extension.

The payroll tax cut has been very popular among voters and analysts have said it could be politically perilous for incumbents to oppose extension of the tax break ahead of next year's election.

Analysts have said a bitter battle during the summer over raising the U.S. debt ceiling and continued standoff between the parties during recent deficit reduction negotiations has fueled anti-incumbent sentiments among voters going into the 2012 elections.

Obama has been pounding Republicans on economic fairness issues in speeches across the county. The reluctance by some Republicans to extend the payroll tax cut has made them vulnerable to criticism that they are the party of the rich.

Republicans have been attacking Obama on the sluggish economy and high unemployment rate and have focused on government spending cuts and overhauling the tax code to reduce top income tax rates.

The Keystone pipeline provision could put Democrats on the spot. Voting against the legislation could expose them to Republican charges that they favor their liberal environmentalist base over hard-pressed workers who are struggling to pay bills.

(Additional reporting by Richard Cowan and Tim Reid; editing by Mohammad Zargham)