Congressional opposition to the D.C. gambling referendum swiftly disintegrated yesterday, virtually clearing the way for the law to become legal on Tuesday.

Early in the day, the House District Committee voted unanimously to reject a proposal that would have overturned the legal gambling referendum passed in the Nov. 4 election.

Hours later, Sen. Mark O. Hatfield (R-Ore.), the key Senate opponent to the legal gambling measure, dropped his plans to seek disapproval of the referendum on the floor of the Senate.

Barring any last-minute challenges between now and next week, when the Congressional review period ends, the District of Columbia could have a legal lottery and a daily numbers game as early as next spring and no later than mid-1982, according to supporters of the gambling initiative.

If the city chooses to go to an "instant" numbers game, in which players buy tickets and rub off covered circles or squares to see if they are winners, that game could begin as early as January of next year.

Although the referendum does not overturn the city's seldom-enforced prohibition against betting on social games such as bridge and poker, it does legalize raffles and bingo games for charitable purposes.

Already, some of those who worked hardest to get the measure approved have begun angling for appointment to the powerful five-member D.C. Gambling Board, which will oversee gaming operations in the city.

The board, appointed by the mayor with the approval of the City Council, will decide what kind of lottery the city will have -- a decision that will means thousands of dollars in contracts to one or more several firms that manufacture lottery tickets and computerized gambling systems. Some of those firms were heavy contributors to the campaign to have the gambling referendum approved.

The board also will draft the regulations that effectivly will allocate dozens of lottery licenses to various business in the city. In neighboring Maryland, where a legal lottery has been in operation since 1973, merchants consider it a financial blessing to be an outlet for the sale of lottery tickets.

For now, the initiative will must sit before Congress through Monday before becoming law. During that time, any member of Congress can try to kill the gambling bill through the unusual step of taking a resolution of disapproval to the full House or Senate. Passage of such a measure by either house would nullify the referendum.

Tom Geterman, Hatfield's chief legislative aide, said yesterday that the Senator now considered it useless to seek Senate rejection of the gambling referendum. "It's fruitless to pursue it at this point. If that's what the District wants, let it be," Geterman said.

Still gambling supporters are not yet breathing signs of relief. "I wouldn't want to bet on anything," Coopersmith said.

"I don't trust Hatfield," said Ron Cocome, coordinator of the D.C. Committee For Legalized Gambling. "He is so flaked out on this issue emotionally," Cocome said he will continue intense lobbying efforts on Capitol Hill in the next few days to blunt any budding antigambling efforts.

The only opposition on the House side came from Rep. Marjorie S. Holt (R-Md.), who pleaded unsuccessfully at the hearing for her colleagues "to sound a note of warning" and overturn the measure.

Holt said she was aware of the reluctance of some members of Congress to reject a referendum approved by city voters. But, she said, "You don't let your children or anybody you feel responsible for go walk off a building."

Several congressmen on that committee said they opposed gambling, but would not support Holt's resolution because they saw no federal interest in the local gambling bill. "I consider it a stupid move, but it is the District's business," said Rep. Stewart B. McKinney (R-Conn.), who said that legal gambling "has torn my state to shreds" with corruption.

Del. Walter E. Fauntroy (D-D.C.), a Baptist minister who also opposed the gambling measure, said he still thought it was a mistake. He added, however, that home rule for the city" includes the right to make mistakes."

The House committee also yesterday rejected a measure that would have overturned a D.C. Statehood referendum approved in November, authorizing the city to convene a constitutional convention to draft a state constitution. That referendum also will become effective Tuesday.