WASHINGTON — House Republicans signaled Thursday that they were backing away from the centerpiece of their budget plan — a proposal to overhaul Medicare — in a decision that underscored both the difficulties and political perils of addressing the nation’s long-term fiscal problems.

While top Republicans insisted that they remained committed to the Medicare initiative, which had become the target of intense attacks by Democrats and liberal groups in recent weeks, the lawmaker who would have to turn the proposal into legislation said he had no plans to do so any time soon.

The lawmaker, Representative Dave Camp, Republican of Michigan and chairman of the Ways and Means Committee, said that while he still supports the party’s Medicare approach, opposition from Democrats made it pointless to proceed.

“I’m not interested in talking about whether the House is going to pass a bill that the Senate shows no interest in,” Mr. Camp said in an appearance at the National Press Club. “I’m not interested in laying down more markers. I am interested in solutions.”