THANKS TO the Supreme Court, the Census Bureau met its deadline yesterday. The justices voted, 7 to 1, late Tuesday to overturn a lower court order that would have postponed the reapportionment process. The bureau promptly responded with its final figures on the 1980 population and with the new allocation of seats in Congress. But that only means the political as well as the legal battle over the Census Bureau's work is now joined.

Almost every state will have its problems in drawing the lines of the new congressional districts. Those problems will be especially acute in New York, which loses five of its 39 seats in the House, and in Ohio, Pennsylvania and Illinois, each of which loses two. Barring retirements, that means incumbent versus incumbent and major fights in the state legislatures over which incumbents go into which districts.

Looming behind the redistricting struggles, however, will be the legal challenges to the validity of the Census Bureau's work. The Supreme Court did not decide any of them Tuesday and did not accelerate any of the pending cases. It simply voted to let the reapportionment process go forward as those cases make their way through the judicial system.

This may not -- as the Department of Justice claims -- make much difference in the allocation of seats in Congress. It told the court that even if New York City wins on its claim that it was grossly undercounted, the adjusted figure is not likely to give that state an additional seat. But any substantial adjustment made in the Census Bureau's count of any major city will have a major effect on how congressional lines are drawn inside that state and on how seats in the state legislature are allocated.

This means that the need for the courts to move speedily in disposing of the undercount issue has not been diminished. The Census Bureau breakdowns of the population by subdivisions of states are due to be published by April 1, and those under attack in the work of a legislature in drawing new district line will be under a cloud. The political problems in each legal problem -- and its inevitable lawsuit -- lurking in the background.