THE BUDGET problem is back where they always drop it off this time of year, with Domenici, Chiles & Co., the steady soldiers of the Senate Budget Committee. The president's proposal was about as advertised: he would pay for defense and reduce the deficit by cutting domestic spending rather than raising taxes. Members of both parties in both houses promptly announced they would never agree to such a budget (though if the past is a guide, they will agree to more than their fuming suggests), and the Senate Budget Committee formally rejected the president's plan.

That means, as the White House was quick to observe, that it is now Congress' responsibility to draw up an alternative. The House Democrats have again said they won't go first. Leadership falls by default to the senators. The Republicans have to bring along their president, the Democrats their party.

The task has been complicated in recent weeks by what in other circumstances might be good news -- new estimates that, left to itself, the deficit will decline by half in five years, from about $200 billion now to about $100 billion by 1991. Time to relax, except that these estimates are not what they seem. They assume the deficit away. It declines this much only if the defense buildup stops and interest costs fall -- but interest costs fall as much as forecast only if Congress reduces the deficit. The process is not quite as circular as it sounds, but nearly. The deficit falls if the deficit falls; you, too, can be an economist.

Everyone knows what the Budget Committee has to do. It must vote to stabilize the defense buildup, then run a good comb one more time through domestic programs. Some small ones we believe can be dropped as the president has proposed. The more important functions, in such fields as health care, student aid and housing, should not be meat- axed as he suggests, but here, too, some useful trimming and tightening can be done. Then the committee must vote to raise taxes by whatever amount is required to bring the deficit into the safety zone.

The Senate panel tried to develop such a compromise last year. For opposite reasons the White House and House leaders shot it down. The committee is about to try again. Every American should wish it well.