They are Capitol Hill's newest political odd couple: the outgoing, suave, self-confident black clergyman from Philadelphia and the intense, rumpled and often fretful son of an Italian-born grocer from Albuquerque.

Except for the shared misery they face as chief negotiators of a far-reaching, complicated and politically tricky deficit-reduction compromise, there is little to suggest a bond between Rep. William H. Gray III (D-Pa.) and Sen. Pete V. Domenici (R-N.M.), chairmen of their respective chambers' budget committees.

Small-state westerner, Republican and generally conservative, Domenici has headed the Senate's budget panel since the GOP took control of the chamber four years ago. He has carefully balanced the often-conflicting demands of the White House and his GOP colleagues.

Big-state easterner, Democrat and as liberal as Domenici is conservative, Gray took over as head of the House budget panel a few months ago, earning high marks among Democratic colleagues for his fledgling efforts at consensus-building within the party.

In public, their only contact has been a bristling exchange in separate appearances before television cameras last month.

Shortly after Gray's committee approved its deficit-reduction plan, Domenici joined Senate Majority Leader Robert J. Dole (R-Kan.) in criticizing it as riddled with phony savings. Gray gleefully tweaked their noses in response, saying he was "disappointed my dear friends Pete and Bob would put on such a display."

The exchange does not suggest a smooth start Tuesday for the House-Senate budget conference, heavily burdened by fundamental disputes over defense spending, Social Security and new cuts in other domestic programs -- disputes that could lock the White House and House Democratic leadership in mortal political combat.

And yet colleagues of the two chairmen say that one of the bright spots in the otherwise peril-ridden negotiations is what one Senate source called their "compatible chemistry."

"Basically they're accommodating people who like working with other people, including each other," said Rep. Vic Fazio (D-Calif.), a House Budget Committee member who has watched both Gray and Domenici in action.

"They're pragmatists, not ideologues . . . . They both believe in getting results," said a Senate Republican.

Moreover, they do not approach the deficit-reduction arena as strangers.

Two years ago, when House-Senate negotiations were near collapse in a bitter political dispute over post-recession spending on job programs, Gray and Domenici got together in a back room over a couple of beers and a pack of cigarettes and cut a mutually face-saving deal that broke the impasse.

With Democrats emboldened by the recession and their gains in the 1982 elections, the Democratic-controlled House was insisting on billions of dollars worth of anti- recession spending, while the Republican-controlled Senate, feeling pressure from the White House, opposed it with equal vehemence.

The Gray-Domenici deal was simple: an $8.5 billion reserve kitty to fund the programs if they were subsequently authorized. With the economic recovery taking the steam out of the Democrats' anti-recession drive, few of the programs were authorized and funded. But both houses had scored political points and, more importantly, a stalemate had been averted.

A few months later, Domenici was hospitalized during a set of negotiations involving transportation appropriations, including a New Mexico road project that the senator, facing reelection the following year, wanted to deliver to the home folks. A Domenici aide approached Gray, who was a House conferee on the measure. Gray came to the rescue, helping to assure the project's inclusion in the bill.

With this background, several prospective conferees from both houses have suggested that Gray and Domenici could resolve their deficit-reduction disputes with relative ease if left to their own resources.

But each has powerful clients: for Domenici, the White House, and for Gray, the House's Democratic majority and leadership.

President Reagan, who agreed reluctantly to defense-spending constraints in the Senate, is holding the line against further compromise, which will undoubtedly be demanded by the House. Dole and Domenici are echoing Reagan's line, at least in public.

Similarly, House conferees can be expected to maintain their opposition to Senate-approved cutbacks in Social Security cost-of-living adjustments.

If the Senate holds firm on defense and the House does the same on Social Security, the result will be far less deficit reduction than the $56 billion for fiscal 1986 approved by each house. Moreover, there are nearly $4 billion worth of differences between House and Senate spending levels for 22 social-welfare programs, such as Medicaid, food stamps, child nutrition and low-income housing. And the Senate would terminate 13 programs while the House would end one: revenue sharing.

Nonetheless, House and Senate sources hold out hope for compromise, partly, they say, because of Gray as the new factor in the equation.

Senators often found it difficult to deal with Rep. James R. Jones (D-Okla.), Gray's predecessor as House budget chairman, in part because he did not always have the Democratic leadership's full backing, which Gray seems to enjoy.

But it is more than just the contrast between Jones and Gray. Basically, it is Gray, whose deft debut as budget chairman not only gave a shot in the arm to Democrats but seemed to charm Republicans, including ranking Budget Committee Republican Delbert L. Latta (Ohio), whose glowing words about Gray contrasted sharply with his normally dour view of Democratic colleagues on the committee.

Senate Republicans are wary but hopeful. "Bill Gray could charm a rattle off a rattlesnake," said a Domenici aide.

House Democrats, who have both won and lost in dealing with the doggedly persistent Domenici, are quick, in turn, to praise the New Mexico senator. "He's formidable in defending the indefensible," said Rep. Thomas J. Downey (D-N.Y.) in what apparently was meant as high praise.

But Downey contended that Gray, despite his relative lack of experience, will be "more than a match for Domenici," an argument frequently made by prospective House Democratic conferees.

"Domenici's going to have his hands full," said Rep. Butler Derrick (D-S.C.). "If he doesn't watch out, he'll wind up agreeing with Bill Gray without even knowing it."