As American businesses feast on federal government contracts, minorities and women are squaring off in a quiet but intense battle over access to some of the leftovers.

The battle centers over a program that, though currently under renovation, does not work. It is a fight that neither the women's groups nor the minority businesses involved want, but one that neither side can seem to avoid.

Though the dispute now involves only business groups and a few people on Capitol Hill, in the administration and in civil rights groups, its autonomy and the momentum it seems to be gaining trouble some observers.

"I would hope that women's groups would sort of reconsider the while thing," said Rep. Parren J. Mitchell (D-Md.), chairman of the Congressional Black Caucus. "This kind of difference of opinion could be the precursor to other things, but I would hope it would stop before it gets to that point."

At issue is eligibility for a Small Business Administration program that sets aside certain high-volume, low-profit-margin contracts for businesses owned by "socially and economically disadvantaged" people.

The conflict is over who is socially and economically disadvantaged.

In March, after heavy lobbying by black businessmen, the House passed a version of a bill designed to restracture the program. It presumes that most blacks and Hispanics are eligible, but would put the burden on women, poor whites and others to prove they qualify.

After failing by one vote to change the eligibility language, women's business groups lobbled successfully for a change in the Senate. Under language adopted by a Senate committee, eligibility would be determined on a case-by-case basis.

If the Senate goes along, the differences will be ironed out in a conference committee. Meanwhile, each side is pressing the White House to endorse the eligibility language it favors.

Women's business organizations look at the elibility question as a matter of fairness. "Women are not participating" in the program, said Dona O'Bannon, president of the National Association of Women Business Owners, noting that 96 percent of the contracts so far have gone to men.

O'Bannon pointed out that SBA was unable to find minority contractors to handle about $86 million worth of contracts offered by other federal agencies for the program, called 8(a), in fiscal 1976.

"The contracts are there, the money is there," she said. "I don't think it's a question of cutting out a piece of the pie" from minorities. "The pie is not really all that small."

She added that the issue has significance beyond 8(a) at a time when the government is searching for a uniform definition of minority.

"Something like this 8(a) bill is going to be significant, in terms of whether you're talking about disadvantaged groups across the board or whether you're talking about disadvantated people," O'Bannon said.

Minority business organizations view the prospect of large numbers of women entering the program as a potential disaster.

"If white women get into 8(a), we can forget it" said Sidney Daniels, legislative analyst for the National Association of Black Manufacturers.

"If procurement agencies ever have to make a choice between dealing with a white firm and dealing with a minority firm, the white firm is going to get the contract, female or not. Cut and dried. We've made a lot of progress in this country, but not that much."

The Carter administration faces a dilemma on the eligibility issue. President Carter has pledged to triple federal purchases from minority businesses this year, and 8(a) is the government's prime vehicle for routing contracts to minorities.

At the same time, he is committed to supporting women-owned businesses, and has asked Cabinet officers to implement a task force report on women in business that explicitly recommends that they be included in the 8(a) program.

"It's a very sticky issue," said a Commerce Department official involved in assessing the issue.

"To be quite honest with you, it's difficult for the administration to take a position when 50 percent of the voters are women, and when minorities contributed so much to the president's election. The administration does not want to make a choice," the official said.

For years there has been talk of potential conflicts between the civil rights and the women's movements, but the two have remained allied on most major issues. The 8(a) program is a curious cause of conflict.

The program is notable mainly for its political origins as the Nixon administration's "black capitalism" initiative, and for its failure at its major task, developing healthy minority businesses.

In 10 years, of the 3,726 firms to enter the program, 149 have "graduated" to independence from government support.

"The underlying reality of what's being talked about is marginal contracts with low profit potential," said Patricia Cloherty, deputy administrator of SBA.

"The symbolism vastly outweighs the reality," Cloherty said. "But the symbol is a commitment to resource flows to groups that previously have not had it."

In the present debate, Cloherty said, minorities and women "are each other's worst enemies. Every time you propose something for one group, it gets knocked out of the park because the other thinks it'll be bad for them."

Ironically, both sides have striven mightily to avoid the fight. The minorities don't think they can win, and the women went to great lengths in the task force report to emphasize that they don't want to compete with them for an admittedly small pot.

"Without sounding maudlin, we could not have been clearer in trying to establish a basis for alliance with minority groups," said Cloherty, one of the report's authors.

No one is certain where the conflict will end. Cloherty views it as a natural phenomenon for two groups trying to wedge their way into the mainstream. "The debate is really on schedule," she said. "It's been aborning for years."

Others see it as a portent of worse to come. "Usually, the women and minorities have been allies," said one of the drafters of the legislation, who requested anonymity.

"Now they're splitting; we may end up with a program that's of no use to anyone, and it can't create anything but bad feelings."