When the Supreme Court hears oral argument today on the constitutionality of the Gramm-Rudman-Hollings budget-balancing law, it will be considering a case that could shape not only the future of the deficit, but the balance of power between Congress and the president.

On one level, the court will decide whether the Constitution permits the drastic procedure at the heart of the law: automatic across-the-board budget cuts mandated to meet targets for reducing the deficit.

These automatic cuts, the heart of Gramm-Rudman-Hollings, were thrown out in February by a special three-judge panel here. Court approval of the automatic trigger mechanism would give new impetus to congressional attempts to forge a budget consensus with less drastic consequences than the billions of dollars of across-the-board cuts under a formula required by the law.

If the court invalidates the trigger, a "fallback mechanism" takes effect under which Congress would have to vote on the cuts needed to meet deficit reduction targets -- something many observers say would reduce the budget law to little more than an unenforceable congressional pledge to do something about the deficit.

Such a ruling would leave Congress close to where it started in its struggle with the deficit, although legislators might feel more public pressure to meet targets specified under the fallback.

On a larger scale, the court's decision in Bowsher v. Synar could redefine if not reshape the relationship between the executive and legislative branches. The decision, expected by July, could be one of the most important separation-of-powers rulings in recent years.

The central issue is the unusual powers the law gives the comptroller general to make the final determinations of how much money needs to be cut.

The problem is the hybrid nature of the comptroller general's job as head of the General Accounting Office. Unlike Cabinet officers, who can be fired by the president for any reason, or heads of independent regulatory agencies, who can be fired by the president for good cause, the comptroller general is nominated by the president but can be fired only by Congress.

Many observers agree that this makes him an "independent officer" within the legislative branch.

The question is whether the law, in giving the power to the comptroller general, gave him too much or gave it to the wrong person. The answer could determine not only the constitutionality of Gramm-Rudman-Hollings, but the status of a host of federal regulatory agencies.

The broadest ground of attack on the law is that it constitutes an excessive delegation of congressional authority. The 11 members of Congress and the federal employe union challenging the law argue that it is unconstitutional because Congress, in enacting its automatic spending cuts, delegated too much authority to the comptroller general, an unelected official.

In passing Gramm-Rudman-Hollings, Congress wanted "to reduce the deficit yet avoid the responsibility for voting reductions in specific programs," attorney Alan B. Morrison argued in his brief to the high court on behalf of the law's challengers. That attempt to achieve "deficit reduction without accountability," he said, should not be accepted by the court.

But the high court has not struck down a law on the grounds of excessive delegation since its battle with President Franklin D. Roose-velt over New Deal agencies in 1935. The special three-judge panel here found that Gramm-Rudman-Hollings passed constitutional muster on delegation grounds.

Although there has been rumbling from some members of the court, particularly Justice William H. Rehnquist, that they may dust off the "delegation doctrine," legal observers on both ends of the political spectrum consider it unlikely that this argument will command a majority of the justices.

The central stumbling block for Gramm-Rudman-Hollings will likely be the narrower question of whether the comptroller general, considered part of the legislative branch, can administer the law, a function reserved for the executive branch under the constitutional scheme.

The three-judge panel struck down the law for this reason, saying the comptroller general could not constitutionally exercise the executive power entrusted to him under the law.

In defense of the law's constitutionality, House general counsel Steven R. Ross argues that the comptroller is not a member of the legislative branch but is an independent officer, somewhat like the heads of regulatory agencies, who are appointed by the president for fixed terms but who cannot be fired at will.

Congress is not shirking its constitutional duties, Ross argues. It made the "hard choices" by exempting certain programs and decreeing across-the-board cuts under its power to enact laws that are "necessary and proper."

Lloyd N. Cutler, representing Comptroller General Charles A. Bowsher, and Senate legal counsel Michael Davidson argue that Gramm-Rudman-Hollings is constitutional because the comptroller is independent of congressional control.

If the fact that only Congress -- and not the president -- can remove him presents a problem, they argue, then strike down that part of the 1921 law setting provisions for removing the comptroller, but don't interfere with his role under Gramm-Rudman-Hollings.

In addition, Davidson argues that the court should not decide questions about power to fire the comptroller unless and until Congress raises the issue by trying to get rid of him.

If the high court bases its opinion on the fact that the comptroller general can be fired by Congress, the opinion could have a narrow impact.

Some conservatives see the case as an opportunity for the court to go further and declare that independent regulatory agencies are unconstitutional because their top officials cannot be fired at will by the president.

Solicitor General Charles Fried, on behalf of the Justice Department, has not gone that far in asking the court to invalidate the law, but has suggested in his brief that at least some independent federal regulatory agencies could be unconstitutional. He argues that under the budget law, the comptroller's duties "are so central to the administration of the executive branch" that they can be performed only by someone the president can fire.

If the court were to adopt that reasoning, it "could have important implications for other agencies," said Harvard Law School Prof. Laurence Tribe. "It would open the question whether, with regard to any given agency, its functions are sufficiently executive in nature that Congress' attempt to insulate it was unconstitutional."