Patrick Andrade for The New York Times

Representative Anthony D. Weiner, Democrat of New York, a fierce champion in Congress of a single-payer health system that would be fully run by the government, said Friday that he had agreed not to insist on a vote on that issue, in an effort to help Democratic leaders pass their plan.

Previously, Mr. Weiner had obtained a commitment from Speaker Nancy Pelosi to allow a vote on a proposal to create a single-payer system like the one used by Canada and many countries in Europe, including England, France and Spain.

Single-payer supporters form a large bloc among liberal Democrats, although there has not been enough broader backing to make the idea politically viable. So Mr. Weiner’s proposal would almost certainly have been defeated, although it would have enabled those liberal Democrats to demonstrate their continuing support for a single-payer system.

But as House Democratic leaders struggle to round up the votes they need to pass their health care legislation, Mr. Weiner said in an interview that it was clear that forcing a vote on the single-payer issue would be counterproductive and could endanger support for the bill at a critical juncture.

Mr. Weiner’s decision to sacrifice the measure also signaled that Democratic leaders may be struggling even harder behind the scenes than they have acknowledged to win votes for the health care legislation. Another sign was a decision to postpone a visit by President Obama to Capitol Hill until Saturday, allowing his personal appeal to have maximum impact on lawmakers as close to the actual vote as possible.

The Democrats’ legislation, which is supported by Mr. Obama, relies on continuing the existing system of mostly employer-sponsored health benefits. The bill seeks to cover 36 million uninsured Americans by expanding Medicaid, the state-federal insurance program for the poor, and by providing government subsidies to moderate-income Americans to help them buy insurance. The subsidies could be used for government-approved private health plans or for a new government-run insurance plan — the so-called public option — that would complete with private insurers.

“I feel very strongly that the employer-based model is not the way to go and single-payer is the better way,” Mr. Weiner said in an interview. “But I never wanted it to be the situation where we literally let the perfect be the enemy of the good.”

He added, “As disappointed as I am, the higher imperative, I think, is making sure that the big bill got passed.”

While Mr. Weiner said he recognized that his decision would disappoint legions of single-payer advocates, he said the danger to the larger bill was too great.

Forcing a vote on single-payer could be particularly problematic for lawmakers who represent districts that split heavily between liberal and more moderate or conservative voters. A vote against the single-payer issue would anger constituents on the left, while emboldening opponents on the right, making it more difficult to support the larger bill. Avoiding a vote on the issue, in turn, could allow centrist Democrats to take a tough vote in favor of the larger bill.

Mr. Weiner said that the debate around the public option had helped the cause of single-payer supporters.

“There’s an old saying in the single-payer movement, God supports the single payer, just not now,” he said. “I think that the public option debate has to some degree advanced the cause of single payer because, in fact, both the proponents and opponents of the public option are in a way stipulating to the point that government-run health care would be more efficient and would be chosen by citizens if it were offered.”

Mr. Obama and Congressional leaders had long ago taken the single-payer issue off the table, saying that it would be too destabilizing to completely change the nation’s health care system. Adopting a single-payer program would require a sweeping overhaul of the tax code, as well as of the compensation and benefits packages of virtually every employer in the United States.

“There is some disappointment,” Mr. Weiner said. “And I would be lying to you if I said I wasn’t disappointed.”