Like two over-the-hill boxers collapsing after a long fight that neither won, the warring factions who sought to control the drive for ratification of the D.C. voting rights amendment are backing off, preparing to go their separate, groggy ways.

Their internal battle over the proposal to give the District two senators and one or two representatives gave conservative foes of the amendment a chance to join forces to carry their campaign to the state legislatures.

Thus, a year after the New Jersey legislature took less than two hours to ratify the amendment, the box score is bleak: six states have ratified the amendment, but 10 have rejected it and many others have ignored it all together. And supporters are no longer talking of achieving a victory in two years -- as they did in the wake of that first ratification.

"I know it's going to be a sad story," said D.C. Del. Walter E. Fauntroy when he was interviewed last week. "We've lost a year, primarily because a small number of people thought my proposal to expand [the coalition that steered the amendment through Congress] was an effort to move them out of a controlling role."

That's one of the few statements Fauntroy has made that leaders of the coalition, Self-Determination for D.C., would not quarrel with. Representatives of Common Cause, the League of Women Voters and other coalition organizations viewed the formation last spring of a quasigovernmental entity, the D.C. Voting Rights Service Corp., as an effort to put Fauntroy, and the city's two other top elected officials, Mayor Marion Barry and City Council Chairman Arrington Dixon, in control.

Coalition members, most of whom represent nonpartisan organizations, said they could no longer put their money and efforts into a drive headed by three elected Democratic officials. So the bickering that had gone on in private since last fall, when Fauntroy was unsuccessful in lining up California as the first yes vote, went public in the spring.

Joseph L. Rauh, the civil rights activist, attempted to mediate the dispute in behalf of the coalition.

"I was a monumental flop," Rauh said Friday. "It doesn't appear to be possible" to get the two factions together. "Maybe like the blacks and the Jews, both will have to go on doing their own thing, and ultimately, they'll come together in a confluence of interests."

Fauntroy's attitude is that he has made his best offer to the coalition: three seats on a nine-member board of directors. As far as Fauntroy is concerned, the coalition can take it or leave it, he's going ahead, "with or without them."

The expanded board allots seats to the delegate, mayor, council chairman, the highest elected Republican official (council vice chairman Jerry Moore), the GOP city chairman, a representative of the business community and three persons to be selected by the coalition.

Meanwhile, the service corporation is "launching a three-month period of preparation for a drive in 1980 in selective states," Fauntroy said.

The battle plan is similar to one Fauntroy put together last fall, and that he now concedes was the beginning of the end of cooperation among supporters, who saw it as too lavish and ambitious -- and too centered on Fauntroy.

His response is that the coalition consists largely of liberal groups that cannot influence the many conservative-dominated legislatures.

"When you need to win in three out of four states -- just look at the map -- you know the coalition can't do it," Fauntroy said. "We must expand our base to get substantive involvement from conservatives, Republicans and groups not normally viewed as progressive forces. Common Cause can't tell conservatives what to do."

Nearly lost in the internecine dispute is whether, on its merits, the amendment can be ratified by 32 more states before the Aug. 22, 1985, ratification deadline.

After New Jersey acted favorably last September, Ohio ratified on Nov. 30, Michigan on Dec. 13, Minnesota and Massachusetts on March 19 and Connecticut on April 11.

The rejections, which can be reversed by subsequent votes, began with Delaware in August 1978, followed by Pennsylvania in November, North Dakota and Wyoming in January, South Carolina, Idaho and Maryland (the latter on a 70-70 vote in the House of Delegates) in February, New Mexico and Arizona in March and New Hampshire in April.

The effort in California typified the sputtering ratification drive. The day after the amendment was approved by the U.S. Senate 13 months ago, Fauntroy flew to Sacramento to urge legislators there to make California the first state to ratify.

In the rush to be first, friendly California legislators attempted to shorten the normal legislative procedures, a maneuver that required approval of two-thirds of both houses. The Assembly passed it quickly, 50 to 19, but even though it got a 22-to-16 majority in the state Senate, it failed to get the needed margin.

This year, following the normal legislative process, the amendment needed only a simple majority, which it got easily last spring in the Assembly. But backers could not be sure they had the needed 21 votes in the Senate, one less than in last year's rush, so the legislature adjourned Friday for the year without bringing the amendment to a vote.

As usual, the rival factions blame each other for the failure in California. Fauntroy said the only reason he rushed to Sacramento last year was that an overzealous Common Cause lobbyist started the ball rolling and then needed help.

The coalition believes the effort failed for a second time this year because Fauntroy refused to use their California contacts.

Opponents have rallied under the auspices of the American Legislative Exchange Council, a conservative organization that published a handbook on why state legislators should reject the proposal.