President Reagan signaled his desire to close out the 1982 battle of the budget yesterday by embracing a plan to cut $4 billion from domestic spending--half what he originally asked--and avoid another clash with Congress.

The compromise spending resolution also restores the White House and leaders of the Republican-controlled Senate to a state of cooperation that was frayed in the debate leading up to Reagan's Nov. 23 veto of a $428 billion spending resolution. The veto resulted in a one-day partial shutdown of the federal government.

Although the new proposal was worked out entirely with Republican congressional leaders and key White House advisers, deputy press secretary Larry Speakes was "hopeful" both houses will accept it.

"I think it has a reasonably good chance," Speakes said.

House Speaker Thomas P. O'Neill Jr. (D-Mass.) sounded unhappy but resigned as he spoke with reporters. He said that the White House still had not contacted him and that the Reagan cuts have gone too deep. "In my heart, I couldn't support them," O'Neill said.

The White House and GOP House leader Robert Michel (Ill.) are working to reassemble the coalition of Republican and conservative "Boll Weevil" House members that passed Reagan's first budget and tax-cut bills, and O'Neill was asked if that coalition could win again over his forces.

"I wouldn't count it out," he replied.

The compromise--in which Reagan got the total dollar savings of $4 billion he had said was the lowest amount he would accept and GOP lawmakers were able to shift the cuts to protect some of their priority social programs--must now be approved by the House and Senate.

O'Neill promised not to obstruct the resolution. Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) said that if the House passes it by Friday, Dec. 11, he will schedule Senate action Dec. 12 and adjourn for the year. That would be days earlier than Congress usually completes a session.

A key factor is that Rep. Silvio O. Conte (R-Mass.) approves of the new compromise. With Conte satisfied that fuel assistance for the poor and other social programs have been relatively well protected, a number of the moderate GOP "Gypsy Moths" may support the compromise.

Without Conte, the president lost by only 12 votes in the House the last time around.

The president "is willing to accept the agreement reached . . . between the House and the Senate and the White House on the continuing resolution," Speakes said. "We are hopeful the continuing resolution will come to the president at this level. If it does, it will reflect adequate savings, in addition to those requested in the original budget, to go halfway toward meeting the requests Reagan made in September."

Senate Republican whip Ted Stevens (Alaska) said: "I think the president has met us more than halfway."

Reagan vetoed the first continuing resolution Nov. 23 because it fell about $2.5 billion short of the halfway point between no cuts and the 12 percent or $8.4 billion he asked for Sept. 24.

After the veto, the president and Congress agreed on a stopgap resolution to continue funding the government at current levels until Dec. 15.

No time period has been established for the proposed compromise resolution, but it appeared likely it would run through the fiscal year to Oct. 1. Speakes said that would be acceptable to the president.

Speakes also said that the president is prepared to sign any appropriations bills that are at or below the spending level of the new continuing resolution.

Reagan signed the first 1982 appropriations bill yesterday, for energy and water development. He said the $12.5 billion achieves almost three-fifths of the savings he requested. "I think it is particularly important that spending for the non-defense programs in this bill is lower than in 1981," Reagan said at the bill-signing ceremony.

As Reagan moved to end the fight over 1982 spending, he and his chief economic advisers held the first of a series of planned meetings on the 1983 budget, which he must present to Congress in January.

Reagan was given an overview of the economy and likely economic developments by Office of Management and Budget Director David A. Stockman, Treasury Secretary Donald T. Regan and Council of Economic Advisers chairman Murray L. Weidenbaum, Speakes said. Speakes declined to reveal any of the forecasts presented to the president, except to say the administration still believes that the first two quarters of calendar 1982 will be flat, but that then the president's economic program will begin to show results.

The president told the 90-minute meeting that he is determined not to lessen his tax cut or change his goal of further cutting federal spending, Speakes said.

O'Neill said that Reagan still has popular support and "we're going to give his program a chance to work."

O'Neill said he considers the program "a disaster." If it is still a disaster in March, he said, the Democrats will present an alternative that probably will include new tax incentives to encourage productivity and capital investment but no new "pump-priming" programs such as job training.

Democrats have sent committees out around the country to gather information for their alternative, which O'Neill said would not be "the old route we went before."

"We're not going to go back to the old ways," he said.