District of Columbia officials argued unsuccessfully with U.S. House members late into the evening yesterday in an effort to rid the massive federal highway bill of a provision they say prevents the District from getting its "fair share" of new federal funds to make critically needed repairs on its major roads.

The House bill, with its nickel-a-gallon increase on the federal gasoline tax, would provide the District with $3 million for road repairs in the coming year -- $1.2 million more than the city currently receives, officials said. But the bill denies D.C. the $10 million share that officials say it is due under provisions designed to help other smaller localities.

The measure was approved by the House shortly after midnight this morning by a vote of 262 to 143.

"We are worried to death about this one do-or-die issue," said Thomas Downs, director of the district's Department of Transportation, before the House vote. He said the $3 million provided in the bill will be "only a drop in the bucket" compared with what D.C. needs to repair roads and bridges suffering from years of neglect, including South Capitol Street and portions of New York Avenue.

While D.C. officials scrambled to win a bigger piece of the enlarged federal pie, Maryland and Virginia officials found much to like in the House bill and the governors of both states had urged their delegations to support it.

Maryland state highway administrator M.S. Caltrider said the state stands to gain about $120 million in fiscal 1983 under the House bill, with large increases both for building interstate highways and rehabilitating other major state roads.

While state lobbyists were carefully combing the House bill and a Senate measure, which contains some substantial differences, to determine which provisions were best for Maryland, Caltrider said, "No matter which bill goes, it will be an improvement" over the present highway funding measures. "Of course, we'd like to see it tailored to our needs," he added, "but it's just a question of being happy or happier."

Hal King, the head of Virginia's Highway and Transportation Department, had calculated that his state stood to benefit by at least $40 million in the coming year, but he reserved final judgment until he could see the final version of the House bill.

As the measure worked its way through Congress, D.C. officials lobbied their position, and they still have one more chance to win the $10 million in road repair funds when the House and Senate meet in conference to work out differences in their versions of the bill. The Senate version contains language favorable to D.C.

The District's argument rests on the issue of how states share the federal highway funds that include the gasoline taxes -- 9 cents a gallon under the new legislation -- funneled from the states into the Highway Trust Fund. The funds for repair of "primary roads," which in the District include such major arteries as Connecticut Avenue, South Capitol Street and 16th Street, are parceled out based on a special formula.

States and territories that fall below a minimum funding level are guaranteed a certain proportion of the fund. Puerto Rico, Guam and American Samoa fall into that category and under the new bill would receive a guaranteed amount. The District, however, which also receives less than the minimum $10 million, would not be allowed to take advantage of the guarantee, according to Downs.

Mayor Marion Barry pleaded in a letter to several House committee chairmen that it is "an issue of basic fairness to the nation's capital." Downs said that D.C. -- whose consumers will pay the increased gasoline tax -- is being treated "like less than the Commonwealth of Puerto Rico, which doesn't even pay gas tax."

Rep. Norman Mineta (D-Calif.), a member of the House Public Works and Transportation Committee who is championing the District's cause, said the major argument against D.C. is that it gets so much more from the trust fund than it puts in. For every $1 in gasoline taxes the city pays in, it gets $4.31 back.

However, Downs and Mineta say that the figure is misleading. Although the city contains only a small percentage of the metropolitan area's gas stations, more than 340,000 vehicles, whose drivers buy gas elsewhere, pour into the city each day. In fairness, they argue,the city should be compensated for the wear and tear on its roads.