UNLESS THE LAW authorizing the appointment of special prosecutors is extended, it will expire in three months. Extension appeared to be a foregone conclusion though, as first the Senate Governmental Affairs Committee in July, and then the House Judiciary Committee in September, reported bills to the floor. But there has been no further movement. Senators are trying to work out a time agreement, but opponents of the bill are stalling. On the House side, the schedule was thrown into confusion this week when one member proposed that the law be extended to cover members of Congress.

The case for covering legislators is a phony. The special-prosecutor law was enacted to deal with conflicts of interest that might arise when one set of high-level political appointees has to investigate another. Any attorney general is in a difficult situation when he has to investigate criminal charges against his deputy, for example, or his colleagues in the Cabinet. But the same conflicts don't exist when he looks into charges brought against members of the other branches. In fact, during this administration several federal judges have been prosecuted and convicted, and so have members of Congress.

Even if a conflict arose, however, and an attorney general had to investigate a congressional leader of his own party, he could still, under the provisions of the existing law, ask for the appointment of a special prosecutor. The 1982 amendments to the law authorize a request in any case in which the attorney general or another Justice Department official has a personal, financial or political conflict of interest. There is no need to require this special treatment in the case of every member of Congress.

A few other issues remain to be settled on the House side. Some opponents of the bill point out that the special-prosecutor law is now being tested in the courts and suggest that it be extended only for a short period of time so that Congress can reevaluate it after litigation has been completed. Why? If the law is found to be unconstitutional -- which we doubt it will be -- it can be abandoned or rewritten. But if it is found to be constitutional, why should Congress have to go through the extension process again a year from now? There is also conflict about the extent to which the attorney general's discretionary powers under the law should be limited. Some compromise should be easy here.

None of the disputed amendments should hang up the House and prevent agreement on extending this important law. The clock is ticking. The bill should be passed.