Democrats insist they have a chance of regaining the House next year. It will not be easy, but the Republican plan to radically reshape Medicare is alienating fence-sitting voters and highlighting the sharp differences between the two parties’ visions of government.

The Medicare argument has certainly been potent in New York’s 26th District, in the Buffalo-Rochester area, where a special election will be held on Tuesday to fill the seat of Christopher Lee, who resigned. Though the district is strongly Republican, the Democratic candidate, Kathleen Hochul, the Erie County clerk, is competitive. The Republican, Assemblywoman Jane Corwin, has had to struggle to defend a highly unpopular policy. The presence of a third candidate, from the Tea Party, is also a large factor in the closeness of the race.

In a televised debate on Wednesday, Ms. Hochul repeatedly accused Ms. Corwin of supporting the House Republican plan to create a voucher system, which, she said, would “effectively decimate” Medicare. Ms. Corwin responded that the plan proposed by Representative Paul Ryan did not involve an actual paper voucher, which is beside the point.

Mr. Ryan would end the government’s guaranteed payment for a set of medical services for the elderly, changing to a system in which the government would simply help the elderly buy private insurance. If health costs went up beyond what insurance would pay, tough luck. Ms. Corwin defended that by saying it would prevent Medicare’s inevitable bankruptcy.