WASHINGTON — The payroll-tax cut that is the largest single element of President Obama's jobs plan has created a political problem for congressional Republicans.

Republicans consider tax breaks a fundamental pillar of their philosophy, but conservatives never much liked the one-year payroll-tax holiday for employees when it was enacted in 2010.

With Obama proposing not only to extend the average $1,000 payroll-tax break for another year but also to increase it by more than 50 percent, many conservative Republicans are promising to resist. They say the $175 billion cost of the tax cut would expand the federal debt unnecessarily, and they are skeptical of administration claims — backed by many private economists — that the move would increase jobs.

House Speaker John Boehner of Ohio and Majority Leader Eric Cantor of Virginia, by contrast, have begun to open the door to compromise on the issue. Republican leaders fear the political consequences if the GOP comes to be seen as supporting tax breaks for everyone except average workers.

Obama is doing his best to stoke that worry. The president traveled to Cantor's home turf in Richmond, Va., on Friday and challenged Republicans to "prove you will fight as hard for tax cuts for workers and middle-class people as you do for oil companies and rich folks."

If Congress fails to extend the payroll-tax cut, virtually all workers will see a tax increase Jan. 1. That not only could be politically unpopular but also might create a drag on the economy.

Yet, many Republicans would prefer to lower taxes on corporations, cut capital-gains taxes or reduce income-tax rates further for individuals. Cutting tax rates in those ways, they argue, would spur more economic growth.

Texas Rep. Pete Sessions, who heads the House Republican campaign committee, called Obama's plan "a horrible idea." He said GOP candidates will have no difficulty explaining why they want to let the tax break expire.

One argument Republicans make against the tax break is that it drains Social Security revenue. Under Obama's plan, money would be transferred from the general fund to cover those losses, but conservative Republicans disagree.

"This is robbing Peter to pay Paul," said Rep. Tom Price, R-Ga., a leading House conservative. "It's a gimmick."

Economic experts, however, warn that failing to extend the tax break would slow the economy by what Moody's Analytics estimates would be a half-percentage point off gross domestic product.

"If nothing is done, every paycheck in the country goes down on January 1st at a very vulnerable moment for the economy," said Chuck Marr, a tax expert and the Center for Budget and Policy Priorities. "Now, everyone gets a pay increase."