President Carter's new $615.8 billion fiscal 1981 ran into a cool reception in Congress yesterday, indicating the administration may have more difficulty than had been thought in keeping its proposals intact.

At a hearing of the Senate Budget Committee both Democrats and Republicans criticized the White House for proposing a 15.8 billion deficit, while GOP senators also lamented the absence of any tax-cut proposals.

Meanwhile, conservatives served notice they will try to increase significantly the step-up in defense programs Carter has proposed, possibly doubling it to 10 percent beyond inflation rather than the 5 percent Carter now wants.

Charles L. Schultze, chairman of Carter's Council of Economic Advisers, said the economy would be able to absorb the extra defense-spending boost without incurring more inflation, but warned other programs would have to be cut sharply.

Schultze and Treasury Secretary G. William Miller also rebuffed GOP suggestions for a tax cut aimed at stimulating new investment. Miller warned the move would "undermine inflationary expections."

Yesterday's session marked the first of some half-dozen appearances Carter's top advisers have scheduled with various key congressional committees. Also testifying yesterday was budget director James T. McIntyre.

The trio will testify this morning before the House Budget Committee, where liberals are expected to berate the administration for not proposing large enough increases in domestic programs.

Yesterday, the United States Conference of Mayors joined the chorus by complaining that the budget did not do enough to aid the nation's cities. However, the group said it still plans to support Carter's budget plan.

The only praise for the administration yesterday came from the Senate Budget Committee's chairman, Edmund S. Muskie (D-Me.), who complimented the White House for "candor" in publicly forecasting in recession.

At the same time, however, Muskie also expressed "disappointment" that the budget does not show a balance. Administration officials have said the budget would be in balance were it not for the forecast of a recession.

It was not immediately clear just how much, if any, the budget panel actually would alter Carter's budget proposals. Muskie and several key Democrats are expected to oppose any increase in Carter's defense budget plans.

In other developments yesterday:

The Commerce Department reported that its index of leading economic indicators, whose behavior is supposed to foretell changes in the economy, remained unchanged in December after falling a revised 1.2 percent in November.

The Treasury announced it plans to raise $2.6 billion in a new cash next week through another quarterly sale of notes and bonds. The auctions will be held next Tuesday, Wednesday and Thursday.