The deepest, most impassioned controversies of the draft registration case at the Supreme Court are the ones least likely to show up in the legal briefs. But they are the ones that may cause headaches for the justice and, inevitably, the aftershock once the decision is made.

A Supreme Court ruling that women must be included by any draft registration program might, first of all, doom the peacetime draft registration program. Congress, reluctant to approve the registration program for men, is considered even more unlikely to vote for one including women. President-elect Ronald Reagan, who came out against draft registration during his campaign, might not even give Congress the opportunity to vote on the issue again.

At the same time, such a ruling would undercut one of the chief arguments used against ratification of the Equal Rights Amendment: that it would mean the drafting of women. Women might have to be drafted regardless of whether there's an ERA.

The least tangible result, however, runs the deepest. Protection of women from the draft, like the special protections they once had from harsh working conditions, puts them on a pedestal which, as one women's rights lawyer puts it, " protects them right out of jobs and advancements and benefits."

With this issue, in Rostker v. Goldberg, many feel the pedestal is more threatened than ever before.

Should the Supreme Court decide to hear the challenge to the all-male draft, the debate is likely to center on the narrowest possible question: Whether Congress' stated reason for excluding women -- "military flexibility" -- is a valid justification for the all-male registration program. But one can tell from the reactions of the anti-ERA forces that much more than this is involved.

"If the court goes wrong on this issue," says anti-ERA leader Phyllis Schlafly, "if it puts the ERA into the Constitution, if the justices up and do it, it will be the greatest example of judicial arrogance in recent times. We are already lining up votes in Congress to withdraw the court's jurisdiction over this issue and I think we can do it. After all, we're within one or two votes of withdrawing jurisdiction over school prayer and I would consider the public indignation in this case to be far more widespread."

Draft registration for women "goes against our entire heritage," says Conservative Caucus head Howard Phillips. "Once you establish the precedent [that women must be registered], the same standards must be applied up and down the line. If it gets to the point where women are drafted, you will have a level of opposition that exceeds anything in the past, greater than opposition to busing, greater than the opposition to abortion, greater than the opposition of the left to the Vietnam War. It just goes against traditions to have daughters drafted into a unisex army."

The pro-ERA lawyers who are piloting the case regard such comments as alarmist overreactions. They point out that registering women does not necessarily mean drafting women and that drafting women does not necessarily mean putting women into combat.

But they acknowledge the symbolic power of a decision requiring female registration. "I think it would diminish one of the leading arguments against the ERA," said American Civil Liberties Union lawyer Isabelle Katz Pinzler, who is a cocounsel on the draft case. The ERA opponents say the constitutional amendment would lead to the drafting of women. "A favorable court decision would point out what's always been true, that Congress has always had the power to register women," with or without ERA, Pinzler said. a

Beyond that, said Judith Lichtman, executive director of the Women's Legal Defense Fund, there is that pedestal. The exclusion of women from the draft says that "they are too good and too virtuous and to fragile to accept those responsibilities. This image is very damaging to the role of women as citizens. The flip side of giving women this special treatment is that they're relegated to second-class citizenship.

"It is like those protective labor laws. What happened with those laws is that somehow they protected women right out of jobs and positions. They hurt us in ways from which we are yet to recover.

"What flows from living up to your responsibilities is an enormous stream of benefits."

The ERA is not the only issue in the draft case boiling beneath the surface. There is the question of the peacetime draft registration program itself.

In fact, the ACLU's involvement in the case stems largely from its opposition to a peacetime draft. If the court upholds the lower-court ruling that women must be registered if men are, ACLU lobbyist David Landau believes there may be no registration at all.

"This case," he says, "is our last, best hope to do away with any idea of a peacetime draft." Congress was reluctant to pass the all-male program in the first place, Landau reasons. If the members, especially after the rightward turn in the elections, are confronted with voting for registration of women, the ACLU hopes the entire program will go down the drain.

Because Reagan opposed the draft registration program, it is equally likely that his administration would not make the effort to reintroduce it after a court decision.