Despite heavy lobbying at the White House by women members of Congress, the Justice Department yesterday asked the Supreme Court to limit federal authority to cut off funds to educational institutions that discriminate against women.

The action, at a time of mounting criticism of the Reagan administration's record on women's issues, has major political ramifications. Women's rights lawyers consider the case among the most important to come to the court in several years. They, along with the women in Congress, had mounted an unusually strong campaign to stop the Justice Department action after a draft of the government's brief was leaked earlier this week.

In the final brief, filed at the court late yesterday in a case involving Grove City College in Pennsylvania, the government took a position that was even more objectionable to women's rights organizations than the draft brief.

A high Justice Department official who asked not to be identified acknowledged that the new brief "tilted a little further away from the women's position," but said it was "solely" a matter of interpreting federal law "on which the lawyering judgment" of Justice Department attorneys "had to prevail."

"I'm tremendously disappointed," said Rep. Claudine Schneider (R-R.I.), one of those who has spent the last few days trying to change the administration's mind. "I think it is both substantively wrong and politically wrong," she said in an interview.

The name of a Justice Department lawyer which had been on the draft brief was not on the final brief made available yesterday. The woman lawyer, Marie E. Klimesz, who had worked on the case earlier, declined comment as did a Justice Department spokesman.

The question that has generated the controversy is whether the receipt of federal financial aid by a specific program at an institution may bring other programs, which do not receive such direct aid, under the sex discrimination law. If the government provides grants for students, as in the Grove City case, for example, may the entire college become subject to the law?

If the government aids a student housing program or provides student grants, for example, does the entire college become subject to the law and to a cutoff of all funds when violations are found?

The difference is crucial in determining the power of the anti-discrimination law.

In yesterday's brief, the government said the "fund-termination sanction" is "limited to the assisted program or activity . . . . The question of Title IX coverage should be resolved not by following to the end of the economic ripple generated by federal aid, but by a common-sense discernment of what, in the most natural way, can be considered the educational 'program or activity' assisted by federal aid." A broader application, the brief said, "would mean that if one student paid for his education with one dollar of federal funds, the entire school would automatically be subject to" the sex discrimination law.

The women's groups, and virtually all other civil rights organizations, believe a much broader application of the law was intended by Congress. Without it, they say, institutions would be free to practice discrimination with a subsidy from the federal government. The 3rd U.S. Circuit Court of Appeals adopted the broader application in its opinion in the Grove City College case. The government's draft brief included only a short statement of the government's position. The brief submitted yesterday expanded on it, directly attacking the appeals court's holding.

The controversy is only a sub-issue of the Grove City case, which stems from the college's refusal to sign an assurance of compliance with Title IX. The government opposes the college in most of the case. Schneider and others had spoken to top White House officials, including James A. Baker III and Michael K. Deaver. White House spokesman Larry Speakes said yesterday that while President Reagan was informed of Justice's intentions, "a brief was not presented . . . . It is being treated as a legal matter."