Congress began work yesterday on President Carter's new fiscal 1981 budget amid warnings from its own economists to heed Carter's admonition against rushing into a traditional anti-recession tax cut.

At a hearing of the House Budget Committee, Alice M. Rivlin, director of the Congressional Budget Office, cautioned that "such a simple prescription" could worsen inflation and hurt the economy in the long run.

Moreover, Rivlin advised in a written report that if the lawmakers do decide on a tax cut they should consider a rollback of Social Security taxes and a speedup in business depreciation writeoff, which would be less inflationary.

She also challenged a proposal by Sen. Edward M. Kennedy (D-Mass.) the Congress enact mandatory wage-price controls. Rivlin said controls would be "least effective in the kind of inflation we've been having."

The cautious tone of the CBO report appeared to jibe generally with the mood on Capitol Hill, indicating that Congress probably will go along with Carter's no-tax-cut recommendation at least for the future.

House speaker Thomas P. O'Neill (D.-Mass.) also decried Kennedy's call for wage-price controls. O'Neill told a press conference yesterday the proposal was "a dead issue, as far as the House is concerned."

CBO also essentially agreed with Carter's basic 1980 economic forecast, calling for a mild recession in the first half of this year, followed by a relatively weak recovery, and little improvement in inflation.

The agency predicted that the economy's output would decline 1.3 percent between now and the end of the year, with the jobless rate rising to 7.7 percent and consumer prices soaring by 9.3 percent.

By comparison, Carter and his advisors have forecast that "real" output will fall one percent, while the jobless rate rises to 7.5 percent and consumer prices jump 10.4 percent. The unemployment rate now is 5.9 percent.

Carter has sent Congress a $615.8 billion budget that calls for a sharp rise in defense spending, continuation of most big domestic programs intact and a reduced $15.8 billion deficit -- all to be financed by allowing taxes to rise.

The president warned that to cut taxes now would exacerbate inflation. Like CBO, Carter aides have said privately that if a tax cut does come they would prefer that it involve Social Security taxes and depreciation write offs.

The action came as, separately, the House Ways and Means Committee began hearings yesterday on proposals to provide new tax incentives for savings and investment -- with vigorous opposition to the plan from the Treasury.

In testimony before the panel, Donald C. Lubick, assistant secretary for tax policy, argued the government already gives savers and investors more than $70 billion a year in breaks, and said new ones would not spur additonal saving.

However, it was not all clear how successful Lubick would be in his attempt to block any new legislation. The committees heard conflicting testmony yesterday from dozens of savings industry represent activities.

And a House-Senate conference comittee already is considering a "small savers'" tax break as part of the pending crude-oil tax bill. Most economists contend the proposal would not increase saving much.

Rivilin's caution against enacting a major income-tax cut now was based partly on the assessment that continuing high inflation and low productivity growth have made traditional economic stimulus tools counterproductive.

The CBO report reviewed the impact on the economy of five widely different economic proposals, from a $21 billion tax-cut-and-spending package to a $20 billion cut in outlays. Its actual economic forecast was based on Carter's proposals.

Although the agency did not make formal recommendations, the reviews showed the plan that seemed to be most effective in case of recession was the one that combined a rollback in Social Society taxes with faster depreciation writeoffs.

Rivlin said in her testimony the nation now may have to pursue "a combination of long - and short-run measures" - and possibly sacrifice some economic vigor in the near term to bring about a healthier economy later on.