The National Organization for Women asked the Supreme Court yesterday to overturn a ruling by a federal judge in Idaho that Congress acted unconstitutionally in extending the ratification deadline for the Equal Rights Amendment.

NOW is also asking the court to resolve the issue as quickly as possible before the June 30 ratification deadline.

NOW was supported by 39 other individuals and organizations--including the AFL-CIO, the Democratic National Committee, the National Education Association, the League of Women Voters and the American Civil Liberties Union--that also are asking the court to decide as quickly as possible. Under a normal schedule, the court might not get to the case until next October.

At issue is the Dec. 23 ruling by U.S. District Court Judge Marion Callister in Boise, Idaho, that the 1978 vote by Congress to extend the deadline by three years and three months is unconstitutional. He also said states may rescind earlier ratifications. Callister is a member and former official in the Mormon Church, which officially opposes the ERA.

Thirty-five of the required 38 states have ratified the ERA, but five have attempted to rescind their votes. Eleanor Smeal, the president of NOW, said yesterday she believes the ERA will win or lose by "a razor-thin" margin.

Under the Constitution, Congress may set any deadline it chooses for ratification, but Callister said Congress should not have changed the deadline. Up to now, Congress has never recognized a state attempt to rescind a ratification vote. Legislation to allow rescission has never been adopted.

Harvard University Professor Laurence Tribe, who represents NOW in the lawsuit, said Callister's decision "is unprecedented in American history. It is the first time a federal court judge or any other judge has derailed the amendment process."

James Fitzpatrick, attorney for House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) and House Judiciary Committee Chairman Peter W. Rodino Jr. (D-N.J.) in the suit, said, "Under our system of separation of powers . . . these matters have been left exclusively to the Congress . . . . The decision is an outright repudiation of the separation of powers on which the government of the U.S. is founded."

The Justice Department is also appealing Callister's ruling, but has announced it will oppose an expedited proceeding.

The department, which is expected to file its appeal early next week, said it would ask the court not to deal with the substantive issues in the case until after the June 30 ratification deadline, saying there is no reason to deal with the substance unless three additional states ratify before the deadline.

However, sources familiar with the case say there is a disagreement between political appointees and career lawyers in Justice over how the case should be handled.

Although the Reagan administration opposes the ERA and favors asking the court not to consider the issue until after the June 30 deadline, the sources say that career lawyers in the office of the solicitor general, which handles appeals to the Supreme Court, would like to ask the court to overturn the Callister decision summarily, something that could be done very quickly.

Solicitor General Rex E. Lee, a Mormon who was involved in the case before he joined the government, has disqualified himself. Lawrence G. Wallace will serve as acting solicitor general in the case.