MINNEAPOLIS -- One by one, America's most generous cities have been adopting a controversial offspring of the sexual revolution, the notion that the homosexual or unmarried heterosexual partners of city employees should be included in the employees' health insurance.

Seattle and the California cities of Berkeley, Santa Cruz and West Hollywood have embraced the idea, but here in what is perhaps the Midwest's most liberal metropolis, the domestic partners coverage plan has hit a snag and provided a critical test of whether the public accepts a national movement to redefine the American family.

"It is essentially a question of fairness," said Minneapolis Mayor Don Fraser, a former member of Congress who supports the contention of many gay and unmarried heterosexual city employees that their companions should have the same access to health care as do their co-workers' spouses.

Opposing fellow Democratic-Farmer-Labor Party member Fraser on the issue is City Council member Walter Dziedzic, representing the conservative side of the broad-gauged DFL caucus that controls the council. Dziedzic, a former police detective, predicted a tense political struggle and an electoral backlash against council members who vote for the bill.

"What is at the root of the ordinance . . . is not the hospitalization and medical benefits," he said, "but the sanctioning of same-sex marriages."

Minnesotans long have celebrated a tradition of maverick, socially conscious politics. The once independent Farmer-Labor Party and the liberal wing of the Republican Party have been respected institutions. Minnesota politicians still call on the spirit of the late senator and vice president Hubert H. Humphrey (D), who as Minneapolis mayor in the 1940s was an early leader in the national civil rights movement.

One recent focus group analysis reported by the Minneapolis Star Tribune argued that Minnesota's pride in its progressive traditions has grown to the point of colossal smugness. "Minnesotans are extremely chauvinistic and, almost to a person, believe that Minnesota . . . is in a class by itself," the report concluded. "Minnesotans believe they are always on the cutting edge of progressive social programs."

But this particular issue appears to cut too close to rock-hard social and religious beliefs, creating the prospect of a debate that may drag for months and end in a 7 to 6 vote on the 13-member council, with neither side certain who will win.

After initial acceptance of domestic partners legislation in other cities and discussion of such ordinances in New York, Denver and the District, resistance also has emerged in San Francisco, where voters blocked an ordinance approved by supervisors, and in Seattle, where a vote is scheduled in November on a domestic partners policy.

Brian Coyle, a gay member of the Minneapolis City Council who proposed the ordinance here, has presented it as a logical response to new social conditions affecting people of every sexual preference. "Over the past 10 years, nuclear families have constituted only about 15 percent of all families," he told the first public hearing on the issue last month. "I think we're trying to acknowledge the demographic realities that we are seeing."

One gay city employee, with a laugh, rejected the notion that homosexuals would use the ordinance to win the right to have legal marriages like heterosexuals. "Are you kidding?" he said. "Yuk! What a model to learn from!"

At the hearing, where almost all testimony was from homosexuals favoring the ordinance, one city employee said she was in effect earning $120 less each month than her married co-workers because she could not use her health benefits to pay her partner's doctor bills.

Many opponents have objected to the potential cost of the measure. "AIDS has thrown a new twist into this, from a cost point of view without the controls to manage what we pay out," Dziedzic said.

But in Berkeley, where domestic partners of city employees have been covered since 1985, Nancy Adler, a city benefits representative, said costs and premiums have not increased. She said about 100 of the city's 1,500 employees have added partners to the coverage, the majority of them unmarried heterosexuals.

Minneapolis has about 5,000 city employees. One city hall expert estimated that as many as 800 might qualify under the ordinance to extend coverage to partners. Under the proposal, each would have to register with the city clerk for a $25 fee and declare the partner to be his or her only domestic partner and not a blood relative.

The two sides have been unable to agree on how much the measure might cost. Estimates range from $80,000 to $800,000 a year.

In an interview, Fraser suggested that at least one council member was seeking a compromise that would reduce the potential cost by eliminating heterosexual partners from the proposed ordinance since they, unlike homosexuals, have the option of qualifying for full benefits by marrying. Coyle reportedly opposes that idea as discriminatory.

Whatever the costs, Dziedzic said, his constituents in northeast Minneapolis, a heavily Roman Catholic area full of descendants of Eastern European immigrants, cannot easily accept the new political influence of the gay community. It has helped to elect one lesbian, Rep. Karen Clark (DFL), to the state legislature and install another, Emma Hixson, as executive director of the city's civil rights department.

Dziedzic said he still is bothered by his failure to persuade pro-homosexual DFL leaders to endorse a black candidate for the school board because the man said he would not favor promoting "gays as role models in the Minneapolis city schools."

"They're making a mockery of family structure, of family values," Dziedzic said.