President Carter, in a last bit of swimming against the political tide, has slashed the Pentagon's request for extra billions to finance military programs in the current fiscal year.

Just before leaving here to spend Christmas in Plains, Ga., the president informed defense leaders that he could not go along with their request for an extra $8 billion for fiscal 1981 and would approve only their "must have" figure of $6.2 billion.

Administration sources said yesterday that, in contrast to past years, defense leaders are taking the $1.8 billion cut without much protest. They realize, officials said, that the president is determined to go out of office projecting a concern for the health of the U.S. economy, even though this latest decision is expected to provoke more screams from the right that he is being soft on defense.

Besides that, the outgoing Pentagon executives assume President-elect Ronald Reagan will ask Congress to increase the fiscal 1981 budget and figure a lower starting point will enable him to look hawkish without engaging in economic overkill.

"We low-balled it," said one defense official in acknowledging that getting the lowest of the three add-ons submitted to the White House is not causing the usual amount of heartburn.

What Defense Secretary Harold Brown had approved as the top add-on for fiscal 1981, after sifting through the requests of the military services, was $8 billion. As is usually the practice, he submitted to the White House that request along with a middle figure, a little more than $7 billion, and a minimum one, $6.2 billion.

About $4.5 billion of the budget money will finance a 11.7 percent pay raise -- plus $150 million to $200 million in other benefits, such as payments for housing in high-cost areas -- given to the military in fiscal 1981. The remainder would cover higher-than-projected inflation.

Although the cost of building barracks and fixing runways is provided in separate legislation, that amount for fiscal 1981, $5.1 billion, will be lumped in with the add-on request going to Congress next month. This means Carter will be asking for supplemental funds of $11.3 billion to go on top of the $160 billion already voted by Congress for fiscal 1981, or $171.3 billion in all.

This $171.3 billion will be the starting point for Reagan's review of how much should be spent on national defense. Many of his advisers want to start new military programs within this fiscal 1981 supplemental rather than settling for amending Carter's fiscal 1982 budget, which will also go to Congress in January.

Option papers have been written for Reagan calling variously for fiscal 1981 add-ons of $10 billion, $20 billion and $30 billion. But William Van Cleave, head of Reagan's transition team at the Pentagon, said in an interview that it would not be wise to distort the fiscal 1981 budget by loading it up with money for new programs. "A supplemental isn't the place for that," he said.

Reagan and his defense secretary-designate, Caspar W. Weinberger, will be trying to ride two horses at once as they try to decrease the federal deficit and, at the same time, make good on campaign rhetoric by building more weapons than Carter did. The ride is bound to get rougher as time goes on because gigantic bills for weaponry on order will be coming in to the Pentagon.

Even under the Carter blueprint, which Reagan assailed as too modest, the Pentagon budget for fiscal 1982 will have to be about $200 billion to fulfill the pledge to provide an after-inflation increase of between 4 and 5 percent a year. And this is before the multibillion-dollar bills for superweapons like the MX missile, Trident missile submarine and XM1 tank pile up in the in-basket.

William J. Perry, the Pentagon executive who has been overseeing the developing and purchasing of super-weapons over the last four years, warned that the new team will have to spread out their new programs to keep the budget from ballooning out of shape or starving the nonnuclear forces. k

Noting that Reagan and/or his advisers have called for building a new bomber and the Trident II submarine missile along with the MX, Perry said: "You try to do all those three things at once, and the tactical forces are going to suffer."