Senate Republicans are vowing to force a vote on a House-passed bill to repeal President Barack Obama’s health care overhaul, despite what appears to be insurmountable Democratic opposition.

Responding swiftly to legislation passed Wednesday in the House by 242 Republicans and three Democrats, Senate GOP leaders are demanding that Majority Leader Harry Reid bring the bill up for a vote in their chamber, which the Nevada Democrat has all but promised not to do. Democratic Senate aides confirmed Thursday that Reid’s stance hasn’t changed.

But Senate Republican leaders are determined. Minority Leader Mitch McConnell (Ky.) virtually guaranteed in a statement Wednesday that he would force a vote, although he has declined to reveal his strategy.

“There are a number of ways to force a vote in the Senate, and Republicans are discussing the options to determine the best path forward,” a senior Republican Senate aide said. “Even some Democrats, particularly those in cycle, would like to take another crack at getting health care right, but so far all they’ve heard from their leadership is ‘unlikely.’”

The GOP aide was referring to the one-word statement — “Unlikely” — issued by Reid spokesman Jon Summers on Wednesday in response to McConnell’s demand for a floor vote on the repeal bill. Reid cannot necessarily block the GOP on his own, but the Majority Leader should be successful in thwarting the minority as long as he keeps his 53-member Conference unified.

Because Obama would veto the health care repeal legislation if it did get past the Senate, Democrats are accusing Republicans of playing politics at a time when millions of Americans remain out of work.

A Democratic Senate aide said the “bottom-line question” to ask is why Senate Republicans are pushing for the repeal. “To get Members to take tough votes? They already have them on record voting for the bill,” the aide said. “So, after all their talk about needing to focus on jobs during the initial debate, why are they so focused on something that will produce no results for them?”

Although Republicans believe in the policy of repeal and intend to cast their health care work as a job-creation effort, there is a political component to their plans.

With 23 Democratic Senate seats up for election this cycle and at least a handful of Democratic incumbents facing the prospect of competitive races, Senate Republicans believe that forcing votes to repeal a bill that has never quite caught on in popularity will help their chances of capturing the majority in 2012.

If enough Democrats join with Republicans to push repeal over the finish line, the GOP scores a policy victory.

Even if Democrats stick together to block the repeal, Republicans still believe they will win political points against Democrats who could be vulnerable on the health care issue in 2012. They include Sens. Sherrod Brown (Ohio), Joe Manchin (W.Va.), Claire McCaskill (Mo.), Ben Nelson (Neb.), Bill Nelson (Fla.), Jon Tester (Mont.) and Jim Webb (Va.).

Just after the health care repeal vote in the House, the National Republican Senatorial Committee blanketed the local media in these Democratic Senators’ states with charges that they were colluding with Reid to prevent a similar vote in the Senate.

“Americans deserve a vote, not a sales pitch, and if Claire McCaskill truly believes most Missourians are on her side then she should step forward and allow the American people to see the votes,” NRSC spokesman Brian Walsh said in a statement. “Every time Missourians hear Senator McCaskill proclaim her political independence, they should look no further than this issue and this debate.”

Senate Democrats, who have been proactive this month in defending the health care law, said Republicans would have to explain their support for repeal to Americans who support many of the law’s provisions, including a ban on denying health insurance coverage because of pre-existing medical conditions.

“Republicans who want to unravel the law that holds insurance companies in check do so at their own peril,” Democratic Senatorial Campaign Committee spokesman Eric Schultz said. “We just wish they could spend a fraction of the energy they’re spending refighting two-year-old political wars on growing jobs or getting this economy moving again.”