Gen. John A. Wickham Jr., the nation's top soldier, has just finished slashing $90 billion out of the Army budget. Yet he views this huge cut in the Army's five-year plan as a minor wound compared with some of the threatening fire coming from a Congress mulling over radical steps to reduce the federal deficit.

Wickham, the Army's chief of staff, said he and his deputies cut the $90 billion under pressure from the White House budget office without canceling any of the tanks, guns and other weapons being bought under the service's biggest modernization since World War II.

Furthermore, the Army's fiscal diet has been accomplished without reducing troops, civilian employes, military training or the kind of family quality-of-life programs the Army has emphasized in recent years, the four-star general added in an interview.

Instead, the savings came from "stretching out" purchases of tanks, helicopters and other hardware, as well as canceling some small programs and buying less ammunition for European dumps. In fiscal 1980, the Army budget was $48.4 billion in constant dollars. Today, it is $81.7 billion.

"This not a time for Calamity Jane," Wickham continued. "We're substantially better off than we were in 1980."

But a growing number of lawmakers are warning that Reagan's rearmament program is about be seriously staggered by the Gramm-Rudman legislation that proposes to impose defense as well as other domestic cuts on the budget in an effort to reduce the deficit. The Army's $90 billion cut, many lawmakers believe, will be only the first of a series required by Gramm-Rudman.

Studies of the impact of Gramm-Rudman are beginning to circulate in Congress and the Pentagon, setting off alarm bells such as Defense Secretary Caspar W. Weinberger's recent declaration that President Reagan would not feel bound to contribute vital defense dollars to the deficit reduction effort. That view has drawn fire from many on Capitol Hill who believe the burden must be shared equally throughout the government.

Sen. Sam Nunn (D-Ga.), ranking Democrat on the Senate Armed Services Committee and a Gramm-Rudman supporter, recently unveiled one study which concluded that if the provision had been enforced in fiscal 1985, Pentagon spending would have been reduced by $13.3 billion.

The cuts facing the Pentagon would have included $4.5 billion in personnel reductions and another $4.1 billion trimmed from the account used to keep the services' tanks, planes and ships operating and repaired.

Illustrating how difficult it can be to pinch Pentagon pennies, Nunn said that tying up half the Navy's ships for a year would reduce the operating account by only $1.4 billion.

Nunn said that Reagan's endorsement of Gramm-Rudman -- with the proviso that the defense budget be allowed to grow 3 percent above inflation -- "indicates that the president isn't living in the real world in budgetary matters. You can't meet the Gramm targets and provide 3 percent real growth in defense without a tax increase. It just can't be done."

"This is not a matter of liberal or conservative, dove or hawk," Nunn told his Senate colleagues. "It's a matter of simple arithmetic. To meet the Gramm deficit targets and still provide 3 percent to the Department of Defense will require at least $80 billion in added revenues over the next four years, according to an analysis provided by the Congressional Budget Office."

Under Gramm-Rudman, a rising deficit could trigger automatic reductions in defense and other kinds of spending. Under such discipline, the military would be lucky to stay on its present plateau during the next five years and could experience significant reductions without a federal tax increase.

Wickham, surprisingly cheerful despite the recent $90 billion cut, finds that prospect considerably more disconcerting. "If all we got were inflation" increases in the budget to stay even, he said, "it would be devastating in the conventional forces."

For example, he said, the Army has bought only half the M1 tanks and Apache attack helicopters and fewer than one-third of the Blackhawk troop helicopters and Bradley fighting vehicles it plans to buy under Reagan's rearmament program.

Without adding any troops to the active force, Wickham said the new weaponry already delivered has given an Army division 18 percent more punch than it had in 1984. Once the other weaponry already on order is delivered, the combat capability of a U.S. division will have increased by 36 percent more than an equivalent Soviet division since 1980, he added.

Reagan, Weinberger and Congress have pushed the military budget to such a high plateau through five years of record increases -- the turnaround started in 1980 under former President Carter -- that the generals and admirals believe their services will be in good shape even if they slip considerably below the administration's original goals.

Wickham based his $90 billion cut on the White House assumption of zero growth -- except for inflation -- in fiscal 1986 and inflation plus 3 percent growth in the subsequent four years. That is considerably less than originally forecast.

Wickham also said the Army has spent money wisely, despite the impression given by military procurement "horror stories."

"The Army takes 4 million procurement actions a year," he said. "If we're 99.9 percent perfect, that still leaves 4,000 screwups. Out of 4,000 screwups there are going to be a horror story or two. Yet we never get credit for the millions that are right."