WHILE CONGRESS struggles over a budget compromise for 1984, another important budget matter is being neglected. That is the choice of a new director for the Congressional Budget Office.

Congress should have made this decision several months ago. CBO's first and only director, Alice Rivlin, announced last fall that she did not want to be appointed to a third term. The budget committees, however, delayed acting on a successor, first on the excuse of the fall congressional elections, then because of the lame-duck session, and then because of the need for continuity at CBO during the first stages of the 1984 budget cycle.

The budget committee chairmen, Sen. Pete Domenici and Rep. James Jones, did manage to set up a bipartisan committee to recommend candidates to the leadership. That was a sensible step toward avoiding a partisan battle over a new director. CBO periodically irritates senators and congressmen from all parts of the political spectrum when its analyses don't happen to concide with their judgments. But the agency has established a well-deserved reputation for impartial and well-informed judgment. Continuing that reputation should be the first consideration in the choice of a new director.

The selection committee, however, has yet to meet, and with its principal members now tied up in the budget conference and its aftermath, no progress is likely for the rest of the month. But the delay in choosing a new CBO director is not only a direct consequence of the protracted budget struggle. It is also a reflection of the deeper conflicts that underlie that debate. As a major instrument and symbol of the process by which Congress now tries to bring its spending and taxing decisions into line, CBO is a target for forces on both the political right and left who find that discipline uncomfortable.

For the president and congressional conservatives, CBO's forecasts are an unpleasant reminder that along with low taxes and big defense spending come big deficits. For old-line House committee chairmen, the budget process and its caretaker, CBO, are major obstacles in the way of spending money for their favorite projects. As the selection process drags on, both sides will have increasing opportunities to press for candidates unlikely to command the bipartisan respect that is needed.

Mrs. Rivlin has obligingly stayed on in her post, but other commitments will require her departure toward the end of July. CBO already lacks a deputy director, since the post has been held open for choice by a new director. With its high-caliber staff, the agency could keep going on its own momentum for awhile. But Congress' inability to decide on a new director would be another unpleasant reminder of its unwillingness to face up to the hard choices of budget control.