WASHINGTON — A Democratic senator, Ron Wyden of Oregon, and a Republican member of the House, Paul D. Ryan of Wisconsin, unveiled a bipartisan plan on Wednesday to revamp Medicare and make a fixed federal contribution to the cost of coverage for each beneficiary.

The lawmakers aim to reshape the debate over the giant health insurance program by addressing concerns that have provoked fierce opposition to similar ideas in the past.

Just as important as the details of their proposal was the fact that the two were working together on an issue that both parties have exploited for political advantage.