WASHINGTON — The White House has indicated that it could accept a nonprofit health care cooperative as an alternative to a new government insurance plan, originally favored by President Obama. But the co-op idea is so ill defined that no one knows exactly what it would look like or how effectively it would compete with commercial insurers.

What is certain is that, as a substitute for a government plan, the co-op concept disappoints many liberals and stirs little enthusiasm among insurers or Republican lawmakers.

And as the White House signaled its flexibility, a contentious debate over the merits of a public plan versus co-ops began playing out in the Democratic Party. Aides to Mr. Obama tried to tamp down concern on the left by emphasizing Monday that the president still supported the idea of a public plan and had not decided whether to drop it.

Some lawmakers said the White House had sent mixed signals, confusing friend and foe alike on Capitol Hill.

Speaker Nancy Pelosi said Monday that House Democrats, rather than backing down, strongly supported giving people the choice of a new government health insurance plan. “A public option is the best option to lower costs, improve the quality of health care, ensure choice and expand coverage,” said Ms. Pelosi, Democrat of California.

As the debate rages, lawmakers are learning that creating cooperatives — loosely defined as private, nonprofit, consumer-owned providers of health care, much like the co-ops that offer telephone, electric and other utility service in rural areas — will not be easy.

The history of health insurance in the United States is full of largely unsuccessful efforts to introduce new models of insurance that would lower costs. And the health insurance markets of many states suggest that any new entrant would face many difficulties in getting established.

Still, proponents of health co-ops are not deterred.

Prof. Ann Hoyt, an economist at the University of Wisconsin-Madison, who has done extensive research on cooperatives in many industries, said they could serve a useful purpose in health care — just as credit unions compete effectively with banks, prompting them to offer higher interest rates on deposits and lower rates on loans.

Professor Hoyt said she had been a member of the Group Health Cooperative of South Central Wisconsin since 1985, and she reported that “the care is excellent.”

Larry J. Zanoni, executive director of the Wisconsin plan, said: “We are a testament to the success of a health care cooperative. But it took us over 30 years to get where we are today.”

The idea of a health cooperative has been pushed by Senator Kent Conrad, Democrat of North Dakota. It has drawn support from centrist Democrats and has intrigued some Republicans.

The government would offer start-up money, perhaps $6 billion, in loans and grants to help doctors, hospitals, businesses and other groups form nonprofit cooperative networks to provide health care and coverage.

The co-ops could be formed at the national, state or local level. Proponents say that a health co-op might need 25,000 members to be financially viable, and at least 500,000 members to negotiate effectively with health care providers.

Health care cooperatives could inject competition in some insurance markets around the country, economists and health policy experts said. But they would need time to buy sophisticated information technology and to negotiate contracts with doctors, hospitals and other health care providers.

Mr. Conrad’s own state demonstrates the uncertainties surrounding cooperatives. Blue Cross Blue Shield of North Dakota dominates the state’s private insurance market, collecting nearly 90 percent of premiums. As a nonprofit owned by its members, the company would hope to qualify as a co-op under federal legislation, said Paul von Ebers, its incoming president and chief executive.

Darren Huber, a spokesman for MeritCare, a not-for-profit clinic and hospital company in North Dakota, said his company would welcome greater competition among insurers.

Any new insurer in North Dakota would probably try to take members from the local Blue Cross plan, but that would not be easy to do.

Representative Earl Pomeroy, Democrat of North Dakota, said the proposal for cooperatives was “a very worthy idea.”

“The market here is uncompetitive,” said Mr. Pomeroy, a former state insurance commissioner. “A cooperative could provide an alternative source of insurance and some interesting competition for premium dollars. A co-op could operate at lower costs, in part because it would not need to pay its executives so generously as the local Blue Cross Blue Shield plan.”

Mr. von Ebers said Blue Cross Blue Shield of North Dakota was examining its compensation policies. “If we wiped out the top 10 salaries in the company, it would make almost no impact on health insurance premiums,” said Mr. von Ebers, who will be paid $500,000 a year, with incentives that could raise that to $750,000.

Hopes for co-ops may also be tempered by the experience of Iowa, home to Senator Charles E. Grassley, the senior Republican on the Finance Committee, which is trying to hash out a bipartisan health care proposal.

In the 1990s, Iowa adopted a law to encourage the development of health care co-ops. One was created, and it died within two years. Although the law is still on the books, the state does not have a co-op now, said Susan E. Voss, the Iowa insurance commissioner.

Wellmark Blue Cross and Blue Shield collects about 70 percent of the premiums paid in the private insurance market in Iowa and South Dakota.

To become established, a new market entrant would have to offer lower prices or better services, Ms. Voss said, adding: “Wellmark has a huge advantage. They already have contracts with practically every doctor in the state.”

Mark C. Stewart, a lawyer in Toledo, Ohio, who represents many cooperatives, said, “If a co-op makes a profit doing business with its patrons, it distributes the profits to the patrons in proportion to the quantity or value of business done with those patrons.”

In a study published in March and financed in part by the federal government, Professor Hoyt and other researchers at the University of Wisconsin identified nearly 30,000 cooperatives with revenues of more than $650 billion a year. They include farm co-ops, retail food co-ops, rural telephone and electric co-ops and credit unions — entities as diverse as Ace Hardware, The Associated Press, Blue Diamond Growers (almonds), Carpet One, Land O’Lakes (dairy products), Ocean Spray (cranberries) and Sun-Maid Growers (raisins).

Mr. Conrad, appearing this week on “Fox News Sunday,” said the idea of a co-op was gaining traction. “It’s not government-run and government-controlled,” he said. “It’s membership-run and membership-controlled, but it does provide a nonprofit competitor for the for-profit insurance companies.”

Insurers have strenuously opposed Mr. Obama’s call for a new government-run insurance plan. Karen M. Ignagni, president of America’s Health Insurance Plans, a trade group, was no more receptive to the idea of co-ops on Monday.

“How will the cooperative be structured?” Ms. Ignagni asked. “What are the regulatory requirements? It may sound benign, but it may use administered prices. I’m not sure it solves any problems.”

Senator Orrin G. Hatch, Republican of Utah, said he saw the differences as more semantic than substantive. “You can call it a co-op, which is another way of saying a government plan,” Mr. Hatch said.