With the Carter administration preparing a budget that will include virtually no new programs, next year's new Congress will turn to a function that it has largely ignored: oversight.

Congressional leaders say the signal from last month's election is clear. "I think there's a real message out there." said House Budget Committee Chairman Robert Giaimo (D-Conn.). "The American people think we can cut and they want us to cut."

"We'll continue in the direction in which we've gone, to reduce the amount of the federal budget deficit . . . and reduce the percentage of the gross national product represented by federal activities," Majority Whip John Brademas (D-Ind.) said.

"I think there will be an intensification of effort to improve the operation of existing programs rather than starting new programs," he added. "I think more attention to oversight ought to be a major thrust of the 96th Congress."

Even national health insurance - promised by President Carter and pushed by Sen. Edward M. Kennedy (D-Mass.) - will probably have to be put "on the back burner," Giaimo said. "I would say new programs and new starts" - on water projects, for instance - "are in for a dreadful time."

In the wake of California's tax-cutting Proposition 13, the last Congress took what one member called "the coward's way out" be refusing to cut specific programs but slashing across the board 2 to 5 percent from appropriations bills. That avoided pressure from various interest groups trying to save their programs. But it also ducked responsibility, leaving the problem of where to cut to the executive branch.

Giaimo thinks that process will continue: "I think Congress likes the idea of across-the-board cuts. It takes the burden of specifying where to cut off its shoulders."

But Giaimo also says that wholesale cuts might not be realistic or necessary as long as inflation increases federal revenues.

Congress has long been talking about overseeing and reviewing programs and agencies, but not really doing it. Oversight is tedious and thankless: reauthorizing programs and enacting new ones had more popular appeal.

But oversight fits hand-in-glove with an antispending, antigovernment mood. Congress have read the antibureaucracy, antiregulations barometer, and, as Brademas said, oversight might be used to "clean up regulations."

In addition, if the cutting mood continues, oversight might be used to build a case for reductions in specific programs. Public airing of funding abuses or program failures could put the interest group on the defensive.

Rep. Ed Pattison (D-N.Y.), just defeated in the election, drew up a class of '74 proposal for more oversight, setting aside a certain period of time for committees to do it. House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) has endorsed the concept.

All this could change, however, in the event of a deep recession. Then government spending might be pumped up to stamp unemployment and stimulate the economy.

Spending bills don't reach the floor until June or July. "An awful lot could happen between now and then," Giaimo said.