Republicans lost a House seat in a Western New York special election on Tuesday, dealing what could be a significant blow to the party’s efforts to reform Medicare.

Erie County Clerk Kathy Hochul (D) upset Republican state Assemblywoman Jane Corwin (R) in the special election in the conservative-leaning 26th district after tying Corwin to the controversial GOP budget plan that included a provision to turn Medicare into a voucher program.

Senate Republicans are still wavering about what to do with the proposal, and Corwin’s loss on Tuesday may provide a chilling effect for Republicans who were already hesitant to embrace the entitlement reform, which polls show is unpopular with the general public.

The Medicare plan, spearheaded by House Budget Committee Chairman Paul Ryan (R-Wis.), has already been the subject of plenty of debate as Republicans in Washington seek deep cuts and debt-reduction measures. And many Republicans, including presidential candidate Newt Gingrich, have at times declined to embrace the proposal.

In New York, the Democrats ran ads early and often on the issue, seeking to overcome a significant registration disadvantage in the Buffalo-area district, which Democrats haven’t held since the 1960s.

In the end, it appeared to have worked, with Hochul winning 48 percent of the vote and Corwin winning 42 percent of the vote with 75 percent of precincts reporting. The Associated Press called the race in Hochul’s favor just more than an hour after polls closed.

“Today, the Republican plan to end Medicare cost Republicans $3.4 million and a seat in Congress,” said Rep. Steve Israel (D-N.Y.), the chairman of the Democratic Congressional Campaign Committee. “And this is only the first seat.”

Even before voters went to the polls Tuesday, Republicans downplayed the significance of Corwin’s performance and particularly the race’s relevance to the debate over Medicare’s future.

“I know this town loves to take signals from individual races. I think the best signal you can take is the 63 seats that we picked up in November,” House Majority Leader Eric Cantor (R-Va.) told reporters Monday.

Cantor and other Democrats cited the presence of third-party candidate Jack Davis in the race. Though Davis previously ran for the seat three times as a Democrat, he ran this time on a ballot line labeled “Tea Party.”

In the end, though, Davis was taking just 8 percent of the vote — slightly outside the margin by which Corwin trailed. That would mean, in order for him to have been the difference-maker, he would have had to be taking votes almost exclusively from Corwin, which seems unlikely given that Davis used to be a Democrat.

Senate Democrats believe that centrist voters in most states reject the Ryan plan to overhaul Medicare by giving its mostly elderly beneficiaries vouchers with which they would then buy insurance on the private markets, and that the conservative support for the Ryan budget will drive a wedge between Senate Republicans and their primary voters.

Senate Majority Leader Harry Reid (D-Nev.) has scheduled a vote later this week on the Ryan budget. At least four Republicans -- Sens. Scott Brown (Mass.), Susan Collins (Maine), Rand Paul (Ky.) and Olympia Snowe (Maine) -- have announced their opposition to the bill, with all but the conservative Paul viewing the Medicare proposal as too punitive.

Reid and Democrats hope that those Republicans who support the Ryan plan, which passed the House on April 15 on a party-line vote, will hurt themselves in general elections next year and in 2014. Those Republicans that oppose the Ryan plan may face political fallout in their GOP primaries, Democratic aides said, explaining the party’s strategy anonymously to discuss internal meetings.

Republicans countered that they believe that voters will reward their “bold leadership” on the issue of swelling federal debt and stagnant job growth.

Republicans have had a rough go of it in recent special elections, even losing a few competitive races in the run-up to their big gains in 2010.

Republicans acknowledge that the current environment isn’t as friendly now as it was in the November elections, but they say Tuesday’s race is hardly the beginning of a Democratic resurgence in 2012.

“If special elections were an early warning system, they sure failed to alert the Democrats of the political tsunami that flooded their ranks in 2010,” Rep. Pete Sessions (R-Texas), the chairman of the National Republican Congressional Committee, said in a statement.

The district became vacant after Rep. Christopher Lee (R-N.Y.) resigned following revelations that he had posted shirtless pictures of himself on the internet classifieds website Craig’s List.