A billion here, a billion there and pretty soon it adds up to real money, so goes the old Washington joke.

In April, the House Armed Services Committee passed a $180.3 billion defense budget, the minimum necessary, committee leaders insisted, to maintain a strong military. Yesterday, the House approved amendments to delete $3.2 billion worth of defense spending from the authorization bill, spurred by the very Armed Services members who only weeks ago had declared nothing was expendable.

It wasn't that the hawks suddenly got religion. Indeed, the incongruous spectacle of such staunch military spending advocates as Reps. Samuel S. Stratton (D-N.Y.), Dan Daniel (D-Va.) and Charles E. Bennett (D-Fla.) sponsoring millions of dollars worth of cuts was for a good reason: their amendments brought the military within the first budget resolution target approved by Congress in May.

Stratton, arguing for reductions in spending for F14 and F16 planes, Airborne Warning and Control System radar planes and ammunition, acknowledged to the House that some "may feel something has gone haywire" but he insisted the cuts did not "damage any major programs." He later added that he was "no patsy" for the Defense Department.

Despite the cuts, the defense bill the House is debating this week represents the largest increase in military spending in U.S. peacetime history. The bill, which authorizes spending for procurement, research and development, civil defense and operations and maintenance, is $46 billion higher than last year's authorization. With yesterday's cuts, it is $6.3 billion less than the Reagan administration request.

Opponents of the bill resorted to colorful metaphors to try to bring the billions into perspective. Rep. Patricia Schroeder (D-Colo.) remarked that it authorizes the Defense Department to spend "roughly $350,000 every minute of next year, day and night, Christmas, New Year's and Veterans Day."

Such arguments fell on deaf ears as the House brushed aside a subsitute bill sponsored by Rep. Ronald V. Dellums (D-Calif.) to spend only $125 billion and stop funding for the MX missile, the B1 bomber, the nuclear aircraft carrier, the Pershing II missile, the ground- and sea-launched cruise missiles and binary chemical weapons.

The Dellums amendment failed, 348 to 55, with all Washington area congressmen voting no. However, several other amendments to delete or reduce funding for the same weapon systems will come up today and are likely to gain wider support.

Schroeder noted that the original bill funded two Trident missile-firing submarines.

"Now the committee argues that one is better policy," she said. "On page 50 of the committee report, we find that the M577A2 command post vehicle should be funded at the requested level. Now, in justification for the Stratton amendment, we learn that this vehicle has not been procured for several years, and no future procurement is planned.

"What I want to know is how much of the remaining $177 billion can be eliminated as wasteful or unnecessary?" she asked.

Rep. Marjorie S. Holt (R-Md.), a member of the Armed Services Committee, argued, however, that even the committee's cuts were "beginning to cut into the muscle of the defense budget . . . . We must resist any further cuts."

The bill provides $89.4 billion for weapons and other procurement, $22.3 billion for research and development, $68.3 billion for operations and maintenance and $252.3 million for civil defense. It does not include spending for military construction, nuclear weapons or selective service which are covered under other legislation.

It sets manpower ceilings at 2,138,300 for active duty forces, 989,000 for the reserves (plus 41,023 support personnel) and 1,050,060 civilian employes.

Among the roughly 50 amendments to be brought up is one by Reps. Norman D. Dicks (D-Wash.) and John J. Rhodes (R-Ariz.) to reduce funds for the Lockheed-built C5B cargo aircraft and use the money to buy Boeing-built commercial airliners.

The two aircraft companies have lobbied fiercely on the issue for weeks. The cargo jets are to carry large equipment such as helicopters and tanks for the Rapid Deployment Force.

Several amendments would delete funds for MX missiles until President Reagan decides on where and how to base them, a subject of much debate since President Carter's idea to run them around race tracks in Nevada proved unpopular.

One proposal, which is cosponsored by Rep. Beverly B. Byron (D-Md.), a conservative member of the Armed Services Committee, would eliminate $1.15 billion for the first nine missiles. This is likely to be the key vote on the MX.

Other amendments would delete funds for nerve gas weapons, Pershing missiles and cut in half the number of U.S. soldiers stationed outside the country.