Federal departments are submitting spending requests for fiscal 1982 far beyond the administration's tentative budget guidelines, apparently on the theory that President Carter is too vulnerable politically this year to turn them down.

If not repulsed, the budgetary onslaught, which involves both Pentagon and domestic spending would push the deficit for fiscal 1982 well above the $45 billion red-ink figure projected for fiscal 1981 -- and possibly near fiscal 1980's estimated deficit of $61 billion.

White House officials concede they will have to slash these initial spending requests sharply to hold the growth of the budget to an acceptable level. The president still hopes to pare spending enough to bring the budget into balance by fiscal 1983, if he is reelected.

Carter has not issued detailed instructions this year on what he wants to spend for major federal programs, in part to avoid making any decisions before the Nov. 4 election. However, insiders say he almost certainly will want to hold the deficit below $40 billion.

Given the tax cut Carter has proposed for next year, analysis say that to hit his target, the president will have to limit the overall spending increase in fiscal 1982 to only what is needed to cover inflation, making this his third essentially "no-growth" budget in a row.

The administration conceded last August that the fiscal 1982 deficit would run at least as high as $36.1 billion. That assumed no spending boosts beyond those needed to keep pace with inflation. An increase of even a few tenths of a percentage point in the inflation rate could add billions more.

The fiscal 1982 budget, to be sent to Congress next January, will essentially decide federal spending no matter who wins the election. Because of the way the budget timetable works, Republican Ronald Reagan would be able to make only minimal changes if elected.

Carter was bound by the same constraints in his fiscal 1977 budget, but he still managed to propose a tax cut for calendar 1977.

Officials say the major difficulty is in the military budget, where Pentagon planners already have served notice that they plan to request several billion dollars more in defense spending than the White House had tentatively targeted for fiscal 1982.

Under pressure from Senate conservatives, Carter already had agreed to allow the defense budget to grow 5 to 6 percent beyond what is needed to cover inflation, rather than the 3 percent "real" growth he proposed last January. However, initial Pentagon estimates would exceed that goal.

There is little expectation, either in or outside the Pentagon, that the Defense Department will get everything it is asking for "They're shooting for the moon," a White House official said. He noted that initial defense requests traditionally overreach their targets.

However, insiders say the same sort of "go-for-broke mentality" is evident in requests from other key departments and agencies, including many that involve major domestic "entitlement" programs -- those with open-ended financing obligations tied to caseloads or population growth.

Some officials speculated that those agencies, whose budgets have been held down for the last two fiscal years, are trying to catch up at a time they believe the president might be receptive.

Normally the budget is pretty far along by this time in the year, but insiders say Carter intentionally has refrained from becoming involved in this budgetmaking until after the election, in part to avoid the kind of controversy that almost inevitably follows presidential spending decisions each fall.

The informal fiscal 1982 budget request submitted by the Pentagon is several billion dollars over previous guidelines in terms of so-called "total obligational authority" to spend in 1982 and in future years.

The estimate the administration published in July for total obligational authority in the military area for fiscal 1982 was $190.6 billion, while overall defense outlays -- involving monies that actually would be spent that year -- were estimated at $172 billion.

White House sources stressed that all of the budget-request figures -- including those from the Pentagon -- are preliminary, informal and highly tentative. Formal requests are not due in until November.

Fiscal 1982 begins next Oct. 1. Fiscal 1981 began last week.