WASHINGTON  In a last effort to give the Senate a bipartisan health care bill, the chairman of the Senate Finance Committee circulated a comprehensive proposal on Sunday to overhaul the health care system and proposed a new fee on insurance companies to help pay for coverage of the uninsured.

The proposal is the culmination of more than a year of work by the chairman, Senator Max Baucus, Democrat of Montana. A similar fee was proposed by several liberal Democrats in July. In making it part of his proposal, Mr. Baucus may help cover the costs of the bill but also risks alienating Republicans whom he is trying to win over. Mr. Baucus is struggling to forge a bipartisan consensus among 6 of the 23 senators on his committee before President Obama puts new pressure on lawmakers in an address to a joint session of Congress on Wednesday evening.

The proposal by Mr. Baucus does not include a public option, or a government-run insurance plan, to compete with private insurers, as many Democrats want.

The White House press secretary, Robert Gibbs, appearing Sunday on the ABC News program “This Week,” said Mr. Obama saw the public plan as “a valuable tool” to promote choice and competition in the insurance market. But he stopped short of saying that the president would veto a bill without it.