WASHINGTON — A potential compromise emerged Wednesday on one of the most vexing issues of the health care overhaul debate — whether to create a new government-sponsored health plan to compete with private insurers.

The compromise offered by Sen. Kent Conrad, D-N.D., would create health care cooperatives owned by groups of residents and small businesses, similar to how electric or other cooperatives operate. They’d be nonprofit, and without the government involvement that troubles Republicans and business groups about the public plan options.

The chairman of the Senate Finance Committee, Sen. Max Baucus of Montana, said Wednesday the idea could be key to a bipartisan health bill. Baucus raised it in a meeting with President Barack Obama, saying later that Obama showed interest. Baucus’ Republican counterpart, Sen. Chuck Grassley of Iowa, also said the concept had potential.

“It’s a way to bridge the gap,” Baucus said.

That’s significant because the dispute over the public plan has been a major obstacle to bipartisan consensus on Obama’s goal of reshaping the nation’s health care system to bring down costs and extend coverage to 50 million uninsured Americans.

Although the Democrats who run Congress might be able to pass health care legislation with little or no Republican backing, Baucus and others say a single-party measure would enjoy less public support and would be less sustainable over time.

Many Democrats, including Obama, strongly favor a new public insurance plan that would, for the first time, offer government-sponsored health care to Americans not eligible for Medicare, Medicaid or other programs. Democrats say this would keep costs down for consumers.

Most Republicans and business groups are just as ardently opposed, saying that private insurers would end up going out of business, unable to compete with a government plan that didn’t have to make a profit.

Conrad’s plan attempts to satisfy both sides. Profit-making insurance companies wouldn’t run the show, but there also wouldn’t be the federal government backing that Republicans fear would eliminate fair competition with private companies. The co-ops could get federal seed money, Conrad said, but that would be the end of federal involvement. The co-ops would negotiate directly with medical providers.

“I’m doing all I can to get a good bipartisan solution, and right now the so-called public option is being transformed into a private alternative to put pressure on insurance companies, hold their feet to the fire, help them keep costs down,” Baucus said. “It may not work. If it doesn’t we’ve got to find something else but right now it looks like it has a decent chance of working.”

Senators stressed many questions remained unanswered because the idea has just surfaced.

“It’s got possibilities,” Grassley said. “There were lots of questions raised about it — not outright objections in our caucus, but a lot of questions.”