The Reagan administration has buried in the budget a proposal to cut drastically the legal fees it pays private lawyers, particularly "public interest" lawyers, who successfully sue the government.

The proposal is designed to save money and cut off what Reagan aides consider another subsidy of liberal social causes. Critics of the proposal said yesterday its primary impact would be to deter lawsuits in such areas as job discrimination, pollution, mine safety and freedom of information.

At the extremes, the Reagan proposal could reduce the fees from more than $100 an hour in some instances to as little as $20 or $30 an hour.

"It could cut the legs off private enforcement," said John Shattuck, Washington lobbyist for the American Civil Liberties Union. "It is obviously designed to hit hardest the public interest groups," said Nan Aron, executive director of the Alliance for Justice, a trade association of public interest lawyers.

"These people," said an Office of Management and Budget official who asked not to be named, "have a remarkable capacity to equate the nation's commitment to justice with the extent to which the taxpayers subsidize them personally."

More than 100 laws include provisions for government payment of attorneys' fees to the prevailing private party as a way of encouraging "private enforcement" of federal statutes. A victim of discrimination in government employment who wins a suit, for example, may be awarded back pay and "reasonable" fees for the attorney who handled the suit.

The amount of the fee is determined in negotiations or by the judge. In Washington, the U.S. attorney's office considers $75 an hour its standard of reasonableness in civil rights cases, according to Royce Lamberth, chief of the civil division.

Under the administration proposal, a "fee cap" would be imposed based on the hourly rate paid to attorneys employed by the government. OMB did not identify that rate in its proposal. But a government lawyer earning $50,000--which is on the high side--earns about $24 an hour.

OMB sources said the proposal was in part inspired by a highly publicized 1980 case in which the prestigious Washington firm of Wilmer and Pickering asked for $206,000 in fees after winning a $33,000 back pay award for 25 Department of Labor employes charging sex discrimination. The court ultimately reduced the fee to $160,000.

Critics said few fee requests come anywhere near that amount.

In addition to capping the hourly rate, the administration would require the fee award to bear "a reasonable relation" to the result achieved in the legal proceeding.

Exempt from the proposal is the Equal Access to Justice Act, designed to help small businesses fight off overreaching government regulators. That act already contains a $75 an hour fee ceiling.