WASHINGTON — A proposal for government-backed health insurance is close to gaining the 60 votes needed to pass the Senate and probably will be in overhaul legislation, a Senate Democratic leader said Sunday.

A proposal for the public option that is gaining wide support would allow states to choose not to participate in a government-run insurance program, said New York Sen. Chuck Schumer, the third-ranking Democrat. The “opt out” proposal is drawing support from many liberal and moderate senators and less opposition from lawmakers wary of government insurance, he said.

Although Democrats control the 60 votes needed to advance legislation under Senate rules, not all Democrats support creating a government-run health insurance program. Negotiations in recent days have focused on crafting a public option that would satisfy liberal and moderate Democrats and not drive away others.

Sen. Ben Nelson, a Nebraska Democrat who objects to a national government-run insurance program, said he would be interested in a proposal that allows states to participate only if they ask to join; He called this approach an “opt in” program. Nelson’s support would be critical in reaching the 60-vote threshold.

Schumer said Senate Majority Leader Harry Reid, D-Nev., is leaning strongly toward an opt-out public option. Reid, who would make the final decision about bringing legislation to the Senate for a vote, led a delegation of Democrats to the White House on Thursday to discuss the issue with President Barack Obama.

Obama has said he strongly supports a public option as a way of driving down costs by providing competition to private insurers. But the president has said it is not essential to achieving the broad goals of health care legislation.

Another approach to creating an alternative to private insurance is setting up nonprofit cooperatives, an idea that has been pushed by Sen. Kent Conrad, D-N.D., chairman of the Senate Budget Committee.

Senate Republicans, who number just 40 in the 100-member chamber, oppose the public option in any form.

“It doesn’t make any sense at all,” said Senate GOP leader Mitch McConnell, R-Ky. “In fact, I think 100 percent of Republicans have indicated they don’t think having the government in the insurance business is a good idea.”

Schumer appeared on NBC’s “Meet the Press,” Nelson was on CNN’s “State of the Union,” and McConnell spoke on ABC’s “This Week.”