A Republican Party that has for decades benefited from a commitment to lower taxes is now finding itself on the defensive on the issue, as members face a deep split over a Democratic plan to extend a payroll tax reduction.

What might normally be a no-brainer for most congressional Republicans is being resisted by many tea-party-conscious members who oppose what they consider a short-term gimmick that would worsen the federal deficit and siphon money from Social Security, which the payroll taxes fund.

Republican leaders fear that the party, which has spent the past year fighting Democrats’ proposals to raise taxes on the wealthy, cannot now allow the payroll tax to increase without handing Democrats a powerful election-year argument that the GOP supports lower taxes only for the rich.

After suggesting that they might vote on a GOP-sponsored proposal this week, Republicans now plan to keep debating the issue in the coming days and are unlikely to vote until next week.

House Speaker John A. Boehner said Wednesday that Republicans will put forward a measure that would renew the payroll tax cut when it expires, but also would require spending cuts that would be used to restore the lost funding to Social Security.

“We have a trust fund that we all know is going broke,” Boehner said. “. . .So if, in fact, you’re going to take money out of the Social Security trust fund, in our view, it has to be replaced.”

Rep. Bill Huizenga (R-Mi.) said he is eager to see what GOP leaders are “cooking up. “Do I want to put money into people’s pockets? Absolutely,” he said. “Am I concerned about the long-term impact this has on the social security trust fund? Absolutely.”  

Republican leaders say they want to find a compromise with Democrats that would keep the payroll tax rate at 4.2 percent next year, rather than allowing it to revert to 6.2 percent — but they reject a Democratic plan to charge a surtax on people who make more than $1 million a year to pay for the tax cut.

Democrats were unable to get the 60 votes necessary in the Senate to advance a $265 billion payroll tax cut proposal last week that would have been funded through a 3.25 percent surtax on incomes over $1 million. A scaled-back $185 billion bill that contains a somewhat smaller surtax also is likely to be killed.

Senate Majority Leader Harry M. Reid (D-Nev.) told reporters Tuesday that the Senate is likely to vote on the Democrats’ latest proposal on Friday.

“I think most Americans, most Republicans, are very reluctant to raise taxes on anyone during this economic crisis that we find ourselves in,” Senate Minority Leader Mitch McConnell (R-Ky.) said Tuesday.

Democrats have proposed lowering the tax even further, to 3.1 percent, saying that the more workers keep and spend, the better it is for the economy.

At that rate, the average family would pay $1,500 less than it would at the 6.2 percent rate, at a cost of $185 billion. If the rate remains at 4.2 percent, the average family will continue to save $1,000 per year.

House leaders are hoping to entice conservative support by packaging the payroll tax extension with other priorities, such as a provision that would make it more likely that construction would begin soon on a controversial oil pipeline from Canada to the Gulf Coast.

But they have yet to find the right formula to attract rank-and-file support. And they’re contending with conservatives who want to institute permanent tax cuts instead of a temporary fix that they think has been unable to stimulate the growth President Obama promised.

“The president’s suggesting we raise taxes on small-business folks to give a temporary one-year tax holiday and make job creators pay it off over the next 10 years,” said freshman Rep. Tim Huels­kamp (R-Kan.). “That’s not the way you grow this economy.”

Rep. Jeff Flake (R-Ariz.) said the American public “understands. . .that Congress has been unwilling to make any tough decisions. We’ve had our cake and eaten it, too, for so long. And this is another example of not being able to say no.”

The Republican division has played out on the presidential campaign trail as well. Former House speaker Newt Gingrich (Ga.) supports extending the tax cut, a spokesman said. So does Rep. Ron Paul (Tex.).

But Rep. Michele Bachmann (Minn.), who voted against the reduction in the first place, is opposed to its extension.

“This is Barack Obama’s idea,” she said on “Fox News Sunday.” “He said that we would create millions of jobs if we lower the payroll tax. That’s not true. It didn’t happen. And his administration admits it didn’t work. So why would you continue a policy that doesn’t work?”

After calling the idea a “temporary little Band-Aid” in a debate sponsored by The Washington Post and Bloomberg News in October, former Massachusetts governor Mitt Romney said Monday that he thinks the tax cut should be extended to help middle-class families. The shift has drawn new charges of flip-flopping from Democrats.

Obama and Democrats have been trying to exploit the GOP division, charging that the party of low taxes does not want them for the middle class.

“Leader McConnell, Speaker Boehner both said they support extending the payroll tax cut. . . . Funny way of showing it, the way they’ve been legislating or nonlegislating,” Reid told reporters Tuesday. “We can’t afford to let the extreme voices in the Republican Party force a $1,000-a-year tax increase for the middle class.”

Some Republicans acknowledge that they’ve been politically boxed in on the issue.

“It’s a heck of a messaging problem,” said Sen. Bob Corker (Tenn.). But, he added, “that’s how we end up, by the way, with so many bad policies in this country.”

Many predict that the tax cut will ultimately be extended as part of a broad bill that would address other budget issues facing end-of-the-year deadlines, such as an extension of unemployment insurance benefits and an adjustment of scheduled cuts to Medicare payments for doctors.

Americans for Tax Reform President Grover Norquist, who helped craft the GOP’s brand as the party of low taxes by writing a pledge for officials to promise not to raise taxes, urged Republicans to extend the payroll tax cut.

Because the rate reduction was designed to be temporary, he said that not extending it would not violate the anti-tax pledge. But he said Republicans shouldn’t let Obama outflank them.

“He wants to use this as an issue,” Norquist said. “Don’t give it to him.”

Staff writer Felicia Sonmez contributed to this report.