Washington — A solemn-faced Sen. Pete V. Domenici allowed himself a quick grin last week as he rode the Senate subway car from the Capitol to the Senate office building for the budget conference. The New Mexico Republican finally had an agreement in his pocket that would produce a federal budget for 1984.
As chairman of both the Senate Budget Committee and of the House-Senate conference charged with striking a compromise, he carried a heavy load of responsibility. If the congressional process of setting spending and taxing limits was to survive, he had to save it.
By last Thursday Senator Domenici had pulled off the rescue, as both houses of Congress, in quick-fire succession, approved an $859 billion budget.
For the hard-working, serious-natured Domenici, the victory was bittersweet. He had been forced to do everything but stand on his head to produce what he called a near miracle, an agreement between a Democratic House and the Republican Senate.
Still unanswered is the question of whether the '84 budget, even though adopted, will be enforced. Sen. Robert Dole (R) of Kansas, whose Finance Committee has the job of implementing many of the budget provisions, has said he doubts his committee can come up with tax bills to raise the $73 billion called for. President Reagan is threatening to veto new taxes as well as spending bills he thinks are too high. And Senate majority leader Howard H. Baker Jr. (R) of Tennessee is promising to support that veto strategy.
Said Senator Dole, ''I guess you can say we've saved the (budget) process, but that's about all.''
As the support from the President, virtually of the House Republicans, and many in the Senate slipped through Domenici's fingers, he found most of his help from Democrats.
At a budget conference meeting, he could be found huddled in the midst of House Democrats. And it was during breakfast with Sen. Lawton Chiles of Florida , the ranking Democrat on his Budget Committee, that he came up with an imaginative answer to a tough problem.
The Democrats were demanding billions of dollars in recession relief programs. The more frugal Republicans would not accept the added spending. So the GOP budget chairman proposed a ''reserve fund'' of $8.5 billion for next year for home and farm mortgage relief, health insurance for the unemployed, and jobs projects. The money cannot be spent unless those proposed bills are passed in Congress and enacted into law.
The reserve fund idea seemed to satisfy both sides and gave Domenici one of several brief moments of optimism as he struggled to forge a compromise. He said as the Senate vote concluded he had been ''very doubtful'' that a budget would pass.
Although he had support from moderate members of his own party, most of the GOP gave the New Mexico senator little aid. The White House turned an icy stare on the budget compromise, which provides for only half of the 10 percent increase in defense spending that the President requested and higher taxes than he wanted. It also includes more domestic spending than the administration wanted.
''The President either wanted to be the pitcher in this game or he'd take his ball and bat and go home,'' House budget chairman James R. Jones (D) of Oklahoma told his colleagues as he led the budget to an almost effortless victory on the House floor. He described House Republicans as throwing rocks at the game but refusing to play.
Republican House members of the conference committee did not participate in the bargaining and refused to sign the compromise agreement.
Even Senate majority leader Baker gave it only lukewarm support, waiting until the last minute to announce he would vote for it. He made the decision only after backing Dole's unsuccessful move to reduce the $73 billion in proposed new taxes for 1984-l986.
As an aide explained, the majority leader backed the budget only to keep the budget process operating and to support the budget chairman.
Domenici, sporting a Ronald Reagan tie clasp, seemed unperturbed by the lackluster Republican support as he discussed his victory with reporters. A moderate conservative who prides himself in his strong record of supporting President Reagan, he pointed out, ''In spite of all the press accounts, in my opinion the President didn't work very hard to defeat the budget.''
The spending compromise preserves the Domenici record of three years as a successful Senate budget chairman, an important factor when he runs for reelection next year. He sees his role in the leadership as a plus in New Mexico.
''The best way to be successful back home in my particular case is to exercise some fiscal leadership for the country,'' he said in an interview earlier this year.