Washington (CNN) -- All kinds of ideas are flying around Capitol Hill about how to extend the payroll tax cut set to expire at the end of the year, but a long-standing battle over tax increases and divisions among congressional Republicans have prevented any from gaining traction so far.
Once again, a clock is ticking. Failure to pass a measure maintaining the lower tax rate assessed on workers would mean a larger tax burden for Americans next year -- $1,000 on a family earning $50,000.
With Congress scheduled to go on its Christmas recess at the end of next week, effectively ending work for the year, pressure is increasing to reach agreement or face public wrath over higher taxes in 2012. Congressional leaders already warn that they may stay longer than planned to work out a deal.
Senate Republicans rejected a Democratic proposal for including a new tax on income over $1 million to help pay for a payroll tax cut extension, even though one of their own -- moderate Susan Collins of Maine -- voted for an initial version of the plan last week.
At the same time, most of the Senate's GOP minority opposed the party's own plan to freeze government pay and take other steps to offset the cost.
On the House side, Republican leaders are trying to work out a deal within their caucus to gain support from tea party conservatives who oppose extending the payroll tax cut at all.
Some House Republicans have discussed using the payroll tax extension as leverage to tack on unrelated measures they want, but President Barack Obama made clear Wednesday he would reject such an effort.
"I think it is fair to say that if the payroll tax cut is attached to a whole bunch of extraneous issues not related to making sure that the American people's taxes don't go up on January 1, it is not something that I am going to accept," Obama told reporters.
A bipartisan compromise offered by Collins and Democratic Sen. Claire McCaskill of Missouri seeks to address concerns on both sides, but it includes a scaled-back version of the so-called "millionaires tax" opposed by Republican leaders.
The proposed compromise has received little support so far, prompting a call to action Wednesday by McCaskill.
"We're confident that we have the right recipe for success here, and if people would quit worrying about winning elections and worry more about trying to get along and get something done, we can get this done in two or three days," McCaskill told CNN.
The issue, a headache for Republicans already, threatens to become a major campaign theme for 2012.
Obama touched on it Tuesday in a policy address in Kansas, saying Republicans protected wealthy taxpayers from a tax increase during deficit negotiations this year, but now threaten to block the payroll tax cut extension. Blocking it would cause most Americans to pay higher taxes next year.
Republicans, who oppose tax increases in keeping with their push to shrink the size of government, argue that Obama and Democrats are forcing votes on proposals they know won't pass in order to score political points.
So far, the public backs the Democratic position, with polls showing majority support for increasing the tax burden on wealthy Americans to help pay for the measure.
Republicans are on the defensive due to their history of arguing that tax cuts end up paying for themselves because they stimulate economic activity by letting consumers keep more of their money instead of giving it to the government.
Democrats are quick to point out that the mounting federal deficits dominating the Washington discussion were caused in part by reduced revenue due to tax cuts from the Bush administration.
Now both parties agree that any measure to extend the payroll tax cut should include provisions to reduce spending or raise revenue to offset the cost.
At issue is the tax on workers that helps fund the Social Security trust fund. As part of a budget-cutting deal last December, Obama and Congress negotiated a reduction of 2 percentage points in the payroll tax rate -- from 6.2% to 4.2%.
With the reduced rate expiring on January 1, Obama and Democrats seek to expand the provision by lowering the rate even further -- to 3.1% -- for another year.
Republicans initially opposed the idea, saying the provision failed to create jobs last year. Republican leaders now say they support an extension, but they differ with Obama and Democrats on how to pay for it.
The latest Democratic plan calls for a 1.9% surtax on income over $1 million, as well as other provisions to cover the $180 billion cost.
Republicans oppose the plan because they say it will increase the tax burden on small-business owners, a contention the White House rejects as false.
House Speaker John Boehner, R-Ohio, said Wednesday that legislation to extend the payroll tax cut must replace the lost revenue for the Social Security trust fund, "and that's a path that we've continued to look at."
Boehner said his caucus would continue its internal discussions Friday to try to come up with a proposal.
In their compromise, Collins and McCaskill included a provision to exempt the income of small-business owners from the surtax. However, House Republicans questioned whether it was possible to legislate such a distinction.
Asked Tuesday about the compromise proposal, Senate Republican leader Mitch McConnell of Kentucky acknowledged the rift within his party on the issue.
"There are differences of opinion in my conference about this, so I'll speak for myself," McConnell told reporters, saying he favors an approach that combines a payroll tax cut extension with what he called job creation steps.
With Collins standing nearby, he added: "Most Republicans are very reluctant to raise taxes on anyone during this economic crisis that we find ourselves in, but there may be others who have a different point of view."
Collins said Wednesday that the plan she proposed with McCaskill offered what McConnell was seeking, such as a provision to fund infrastructure projects that would create construction jobs.
"What the minority leader (McConnell) said is very consistent with our bill," Collins told CNN. "It does not raise taxes on middle-class families, and it does create jobs."
She called for Congress to move past politically inspired votes on measures with no chance of passing.
"It simply gets us nowhere and is discouraging to employers and the American public at large when we keep having these partisan votes," Collins said. "So what we're trying to do is bridge that divide."
The revised Democratic proposal unveiled Monday by Sen. Bob Casey, D-Pennsylvania, contains a reduced version of the "millionaires surtax," down to 1.9% from the original 3.25%, and calls for it to expire after 10 years, according to a statement by the senator.
In addition to revenue from this surtax, the new proposal would be paid for by increasing fees that Fannie Mae and Freddie Mac charge mortgage lenders to guarantee repayment of new mortgage loans, Casey's statement said.
The provision was discussed during negotiations by the congressional "super committee" that failed to reach a deficit reduction deal last month, and would raise $38.1 billion, according to Casey's statement.
House Republican leaders are trying to assemble their own proposal to extend the payroll tax cut in conjunction with other steps.
However, a group of fiscally conservative Republicans opposed the GOP leaders' plan because the offsetting spending cuts would take a decade to complete.
House GOP leaders said Wednesday their talks were continuing, with no proposal expected to emerge for action this week.
CNN's Ted Barrett and Deirdre Walsh contributed to this report.