The House Budget Committee is scheduled to begin work today on a fiscal 1981 budget plan that would outdo President Carter's proposal in cutting spending and also would provide for some 1981 tax cuts.

Worked out in a caucus of the panel's Democrats, the plan calls for $16 billion in spending cuts, compared with $13 billion to $14 billion proposed by the White House. The congressional cuts would produce a budget surplus of $1.3 billion.

The Democrats balked at Carter's additional request to hold in reserve an estimated $11 billion in new revenues expected from his oil-import fee, and decided to earmark the money instead for business and Social Security tax cuts.

The tax cuts would not take effect until Jan. 1, but making room for them in the budget resolution would allow the tax-writing committee to propose them immediately. Carter has said he wants the budget balanced first.

In other developments:

Several of the nation's largest banks raised their prime rate -- the interest they charge their most credit-worthy corporate customers -- to 19 percent, from 18 1/4 percent. The rise was the second in less than a week.

Fresh government statistics showed that several key sectors of the economy are weakening, indicating that the long-heralded recession may be here. Housing starts plummeted 6.3 percent, while consumer spending fell.

The nation's financial markets recovered from their initial negative reaction to the president's new anti-inflation proposals.The stock market shot up 12 points yesterday, while the bond market also edged up.

Meanwhile, Carter continued to receive criticism on his proposed budget cuts from liberal Democrats dissatisfied with his reductions in aid to cities, amid signs that the White House might pull back from some of its original proposals.

At the same time, Federal Reserve Board Chairman Paul A. Volcker appealed to Congress to cut spending more than either congressional leaders or the White House have said they will.

"The quicker we get through this period, the better," the Fed chairman told the Senate Banking Committee in a hearing. Volcker also opposed any tax cuts now. He did not specify how much he thought Congress should cut spending.

Carter's budget-cut proposals became a political issue in New York yesterday as Sen Edward M. Kennedy (D-Mass.) decried the president's decision not to detail his proposed cuts before the March 25 New York primary.

Mayor Edward Koch was also primed to protest the forthcoming cuts. But the White House managed to head this off as Vice President Mondale promised to send Koch detailed information on the president's plan within 24 hours.

Koch had been scheduled to hold a news conference to complain that the cuts would prevent the city from balancing its budget, but he canceled it abruptly after receiving Mondale's call.

Sources said White House domestic adviser Stuart E. Elizenstat has been pushing to offset Carter's proposals for reductions in aid to cities with a new package of aid for "special" cases like New York's.

Kennedy, stumping in New York City yesterday after the start of the Illinois primary, called Carter's decision to withhold specifics of his budget cuts "one of the most cynical aspects of this campaign."

Meanwhile, Rep. James H. Scheuer (D-N.Y.) yesterday canceled an 11:45 a.m. meeting with Carter, in which he reportedly had planned to endorse the president for reeelection. Koch already has said he will back Carter.

The spending cuts recommended by the House Budget Committee Democrats were expected to parallel a list of proposed reductions agreed upon by House and Senate leaders in discussions with the White House last week.

Among the major cutbacks are $1.7 billion from ending the states' portion of the federal revenue-sharing program, $1.6 billion in cuts in public jobs and youth programs, and $1 billion in antirecession aid to cities.

The list also includes eliminating Saturday mail delivery, computing cost-of-living increases for federal retires once instead of twice a year, and cutting grants to state and local law-enforcement agencies.

The proposal worked out by the committee's Democrats still must be approved by the full panel. The committee is to begin formal drafting this morning in what is expected to be a politically heated session.

The proposal to earmark most of the $11 billion in oil-import-free revenues for 1981 tax cuts was pushed through at the request of the budget panel's chairman, Rep. Robert N. Giaimo (D-Conn.).

Although Carter has asked that the import-fee revenues be held as insurance against congressional failure to balance the budget, Giaimo said he feared that simply keeping the money in reserve would invite lawmakers to vote down spending cuts.

Volcker told the Senate Banking Committee in testimony yesterday that, while he generally applauded Carter's proposals to cut spending by $13 billion, he would "enthusiastically welcome" efforts to slash the budget even further.

He also made clear that he has no love for even the limited form of credit controls that the semi-independent central bank has imposed at Carter's request, on some types of consumer borrowing.

And, under questioning by Sen. Jake Garn (R-Utah), he flatly said the Fed would not impose more specific controls, such as putting a cap on business borrowing or specifying minimum down payments for loans.

"We haven't done any of those things," he said. "I don't like those things. I have no intention of using any of those things." He called the use of controls generally "extraordinary and temporary."

Volcker also denied that he had suggested the use of controls to the administration. Asked by Garn whether he had formally opposed them, Volcker replied, "We had some discussion extending over a period of time."

At one point, Volcker also cautioned committee members that he could not guarantee that sectors of the economy such as housing and small business would escape all impact from the new credit restraints, despite safeguards now in force.

While the Fed has shaped its controls program primarily to limit lending to bug business, not small, Volcker said "we cannot avoid impacts on housing and small business and we probably should not eliminate all the impact."