In a new round of political horse trading, Senate Democrats are offering up a modified version of their payroll tax cut extension, one which pays for itself in a GOP-friendly manner, in order to increase the odds of its package.

Democratic officials told the AP Senate Majority Leader Harry Reid, D-Nev., will introduce a revised plan that will eliminate the proposed payroll tax cut for employers, which would remove about $70 billion from the cost of the plan.

It will be a compromise - a compromise between the Republican approach and our approach, a Democratic aide told Reuters. It will be very difficult for Republicans who want to be on the right side of this issue to vote against it.

The legislation has become the centerpiece of political wrangling and partisan sniping since its introduction last week.

The original bill would have lowered the rate to 3.1 percent, covered by a 3.25 percent increase on higher level incomes. The plan failed in a vote, as well as a Republican counter which would have cut the federal workforce.

The revamped version, aside from removing the cut in employers' share of the tax, would also find funding from spending cuts that never survived the budget deficit super committee. It also retains the original tax on millionaires, though at a reduced rate. It will also adopt the GOP proposal's portion that limits social safety net benefits for the wealthy.

The bill will be brought before the Senate for a test vote later this week, with a second GOP version reportedly in the works.

The bill will most likely fall into a larger package that will also extend unemployment benefits, as well as include some pet Republican projects. The GOP reportedly tried to link the tax cuts to the Keystone Pipeline approval over the weekend, in an effort to garner support from House Republicans.

House Minority Leader Nancy Pelosi, D-Calif., reportedly said such efforts would be fruitless, according to TPM.

It's unworthy of the needs of the American people for them to go all around the mulberry bush with this stuff, Pelosi said. If they want to do something for the American people -- to remove the uncertainty as to whether these payroll tax cuts will be extended, whether [unemployment insurance] will be extended ... let's just get about doing it.

The battle has pitted Republicans against a tax cut which they said should be paid for, which they have argued for years lowering taxes pays for itself.

This is a moment, Pelosi said. They want to give tax cuts to the wealthy which they say shouldn't be paid for, and should be permanent. And they don't want to extend the payroll tax [cut] for middle-income people -- but if they do, they should be paid for ... I mean, it's a stunning thing.