Defense Secretary Caspar W. Weinberger yesterday signaled that the administration will try to stave off cuts in its record high defense budget by warning Congress that thousands of jobs are at stake.

"While it is not a reason for defense spending," Weinberger said at the National Press Club, "we must remember that at least 350,000 jobs are at stake and will be lost if there are drastic cuts."

Navy Defense Secretary John F. Lehman Jr. has been issuing similar warnings about the consequences of congressional cuts in the administration's shipbuilding budget for fiscal 1983, which includes two nuclear-powered aircraft carriers.

Weinberger, when asked yesterday about military leaders who have testified that there is not enough money budgeted over the next five years to implement the defense guidance they are receiving from civilians, said, "We don't have much option to rethink our program."

The defense secretary added that if critics believe more money is needed to carry out administration military policy, "someone should introduce a supplemental" for additional funds for the Pentagon.

A study released yesterday by the Council of Economic Priorities took issue with Weinberger's assertion that the defense budget could provide a lift to the national economy. Said the council:

"The administration's five-year, $1.6 trillion buildup, which will cost the American family $22,000, could seriously damage our long range prospects for economic prosperity."

Alice Tepper Marlin, council director, contended that "clearly, our national security would be well served by substantially reducing the administration's runaway arms budget."