The Senate Armed Services Committee last night approved all but about $2.8 billion of the $257 billion President Reagan requested in defense spending authority next year after a fierce argument behind closed doors over buying at once the two nuclear aircraft carriers he wants.

The committee action fell far short of Chairman John G. Tower's (R-Tex.) pledge to the Senate Budget Committee to try to keep defense spending $2 billion below Reagan's request for fiscal 1983. That large a cut in spending would require about an $8 billion cut in authority.

As the mark-up concluded last night Tower told his colleagues he would look for additional places to cut the military construction and pay bills also handled by his committee. The decline in world oil prices will also save the Defense Department money, he predicted.

The Pentagon budget is the leading target for many in Congress seeking to reduce the projected deficit of over $100 billion next year. But Reagan has refused to let his budget ax fall on defense programs, setting the stage for fights on the House and Senate floors when the Pentagon procurement and appropriations bills come up for passage.

The shouting behind closed doors during the Senate committee's session yesterday indicated that Reagan's request for $6.87 billion in fiscal 1983 to build two nuclear-powered, Nimitz class aircraft carriers at once will be hotly contested in coming weeks.

Sen. Gary Hart (D-Colo.) first tried to get the committee to earmark Nimitz money for smaller aircraft carriers, but then Sen. William S. Cohen (R-Maine) proposed to fund one Nimitz carrier and put off the second. Only after that motion had carried, 10 to 4, sources said, did the Democratic senators learn that the Cohen amendment would have authorized both carriers, with the second funded a little at a time rather than all at once.

Hart argued that such incremental funding would set a bad precedent. Sen. Harry F. Byrd Jr. (Ind.-Va.) and Cohen got in a shouting match during the closed door carrier debate, sources said, as tempers flared all around the committee table. In the end, the Cohen amendment died on an 8-to-8 vote, meaning both carriers were authorized but by the slimmest of margins in a committee highly supportive of the Pentagon.

The $2.8 billion net reduction in budget authority--money appropriated in one year but often spent over several--was achieved through cuts in various programs, including:

MX missile. The roughly $2 billion requested to install the first 40 of these giant missiles temporarily in existing Minuteman silos was denied on the ground that this amount would be better spent on the permanent basing scheme after Reagan decides what it should be.

Army AH64 attack helicopter. All but about $73 million of the $998.7 million requested was denied, with the understanding the program could go forward next year if problems were brought under control.

Air Force A10 antitank plane. The committee decided there was no need to buy the 20 additional planes for the $376 million requested. Much of the A10 is built by Fairchild in Hagerstown, Md.

Smaller cuts were made in the Air Force Maverick air-to-ground missile and Army Infantry Fighting Vehicle program. The committee added money to buy more F15 and F16 fighters than Reagan requested and directed the Navy to buy electronic warfare versions of the A6 attack plane, the EA6B, instead of the A6.