The White House opened the door to compromise yesterday on President Reagan's much-criticized 1983 budget by offering to study a budget proposal by Senate Budget Committee Chairman Pete V. Domenici (R-N.M.), which it labeled "a good faith effort to come up with a comprehensive alternative."

The signs of compromise came as further criticism was heaped on the president's budget yesterday by House Democrats who declared it "mean spirited" and "cruel," and signaled their reluctance to go along with many of the proposed cuts in social programs. At oversight hearings of the House Ways and Means Committee, Democrats sharply attacked Health and Human Services Secretary Richard S. Schweiker and Labor Secretary Raymond J. Donovan for indifference to the poor.

So far, Reagan has refused to back away from two key elements in his budget that have come under the most fire in Congress: the proposed big buildup in defense spending and staged cuts in individual income taxes. Domenici's plan, which is aimed at cutting the federal budget deficit in fiscal 1983 and beyond, would shave $20 billion to $25 billion through fiscal 1985 from defense outlays and raise $18 billion in 1983, $49 billion in 1984 and $55 billion in 1985 from tax increases.

The 1983 deficit under this plan would be $92 billion, Domenici has said. He also suggested freezing many domestic spending programs, along the lines of an earlier proposal from Sen Ernest F. Hollings (D-S.C.), ranking Democrat on the Budget Committee.

Budget Director David Stockman said there were some "problem areas" in Domenici's proposal and White House Deputy Press Secretary Peter Roussel said "we do have some obvious concerns about it: the specifics of how he would raise the revenues and the impact upon economic recovery, the impact of his defense plans upon our national security and whether there would be any unintended adverse impact of his proposed spending freeze."

However, this reaction was much more conciliatory than the response to Hollings' proposal, which Treasury Secretary Donald T. Regan called "ridiculous." Regan told the Senate Budget Committee yesterday that he believed Domenici's plan was "very interesting" and "reasonable."

Reagan's budget has been attacked by both Republicans and Democrats for including too big a deficit, an excessive increase in defense spending and harsh cuts in domestic spending. Many experts also question whether the deficit would stay at the $91.5 billion predicted by the president for 1983, and $83 billion in 1984 even if Reagan were to win all his proposed savings. Domenici's plan aims for a similar 1983 deficit, despite bigger budget savings, as the senator says Reagan's deficit is too optimistic.

Congressional Budget Office director Alice Rivlin told a Senate panel yesterday that the projected savings in the budget from selling off-shore oil leases and from employing more Internal Revenue Service agents seem too high. The CBO expects $5 billion less from the accelerated sale of the oil leases, she said. The CBO has predicted larger baseline budget deficits than the administration.