The House Budget Committee last night handed President Carter a speedy first-round victory on his new anti-inflation package, approving a fiscal 1981 budget plan that calls for $16.4 billion in spending cuts, $2.4 billion more than Carter requested.

However, in a last-minute bid to win Republican votes, the panel agreed to earmark in effect $11 billion in new revenues from Carter's oil import fee for cuts in business and Social Security taxes next January, rather than holding the money in reserve as Carter requested.

The gesture to the GOP came when liberals on the panel defected after resounding defeats on attempts to trim defense spending and restore some of the proposed cuts in key domestic programs.

Annually, Congress must pass a first budget resolution by May 15 setting targets for next fiscal year. By Sept. 15, it must pass a second resolution setting binding totals. It cannot then exceed these totals without expressly amending them.

The budget resolution was approved, 18 to 6, with Republicans, for the first time in the five-year history of the congressional budget process, joining moderate and conservative Democrats in supporting the measure. All of the panel's liberals opposed it.

The tax-cut proposal would allow up to $20 billion worth of tax reductions but only to the extent that the budget is in balance.

Carter has hinted that he might support a limited tax-cut plan, but has warned it would have to wait until the deficit is eliminated. If there is room in the budget ultimately, yesterday's resolution would permit a tax cut of up to $20 billion a year.

Although the tax-cut plan was proposed formally by Republicans, the details were worked out by conservative and moderate Democrats, led by Rep. James R. Jones (D-Okla.), a member of both the Budget and Ways and Means committees.

The liberals' defection is expected to guarantee a bitter fight when the budget resolution reaches the House floor.

Rep. Louis Stokes (D-Ohio), speaking for the Black Caucus, warned the panel: "I can asure you there will be 17 votes against" on the floor. Stokes said he was "ashamed that the Democratic Party has come to the point that it will vote" cuts in so many programs.

The attempts by the Liberals were defeated 19 to 6 and 19 to 8. The committee first voted down efforts by Rep. David Obey (D-Wis.) to reduce defense spending. The liberals then tried unsuccessfully to restore $4.5 billion in domestic outlays and add $4.5 billion in tax "reforms."

The group's final defeat came on White House-backed move, endorsed by Majority Leader Jim Wright (D-Tex.), to reduce a planned $1.7 billion cut eliminating the states' portion of revenue sharing. That proposal was defeated 12 to 12 with the help of Budget Committee Chairman Robert N. Giaimo (D-Conn.), who refused to use a proxy from liberal Rep. Norman Minetta (D-Calif.).

That prompted Obey to shout: "Remind me never to give you my proxy." Giaimo shot back: "You'll never get the chance."

Later, the chairman declared sarcastically: "On that note, the Jimmy Carter New York primary amendment fails" -- a reference to allegations that the White House was backing the amendment to help Carter in the New York primary next Tuesday. Some skeptics have charged that Carter is withholding specifics of his budget-cut proposals for the same reason.

The budget the panel approved last night includes $16.4 billion in spending cuts, mostly in key domestic programs, with outlays of $611.8 billion and a surplus, the first since 1969, of $2 billion.

The budget cuts include the states' portion of revenue sharing, $1 billion in antirecession aid to cities, money for public service jobs, a tightening of the food stamp program, delay of welfare reform, cuts in child nutrition, elimination of Saturday mail delivery and a federal hiring freeze.

Also in the measure is the elimination of $150 million in start-up money for Carter's new youth unemployment program which was to have been the centerpiece of the president's election-year domestic program.

Without the liberals, mainstream Democrats on the House Budget Committee would need to bargain with Republicans for enough votes to send a resolution to the floor, and to pass it there.

The liberals threatened to bolt after losing on a series of motions to cut defense spending more than Chairman Robert N. Giaimo (D-Conn.) has proposed. They want to shift the defense money to social programs.

The committee approved Giaimo's recommendation of $147.9 billion in defense outlays.

That is $1.7 billion more than President Carter proposed in his initial budget in January, which was already some $16 billion above this year's estimated spending level.

But the Giaimo recommendation is about $1 billion less than congressional experts think Carter's proposed defense program would actually cost, given likely inflation rates next year. Carter's first budget assumed lower rates.

Giaimo finally appealed to the liberals to stop, saying: "Let's face the reality. There is overwhelming support in this Congress for defense and you're kidding yourselves to think you're going to cut" defense spending.

He conceded that "you have a right to be" angry about the defense spending: "The anguish and suffering are not being shared equally." But he noted there were pressures in the Senate to raise Pentagon spending higher even than he has proposed.

Earlier, liberals did fend off a motion by conservatives to eliminate the legal services program for the poor. Rep. William Brodhead (D-Mich.) burst out at the group: "Hell, anybody can vote for a cut in legal services for the poor. There's no political problem in voting to kick the hell out of poor people."

Giaimo ultimately held his budget plan intact by appealing to the group to hunker down against all efforts to upset it, from any quarter. "We're being hit by every constituent group possible," he complained. "They're coming in on airplanes faster than they can land."

All told, Giaimo proposed about $15.9 billion in program reductions to produce his small projected surplus. Most of those reductions were in domestic programs.

The developments came as Commerce Department preliminary rough estimates showed that the economy grew at a 2 percent annual rate in the first quarter of this year, indicating that the long-predicted recession still has not begun.

On Capitol Hill, Federal Reserve Board Chairman Paul A. Volcker urged the Joint Economic Committee at a hearing yesterday to shelve proposals for tax cuts until after Congress has formally balanced the budget. Volcker said that, with recession nowhere in sight, inflation-fighting still has highest priority.

Separately, Senate Democrats agreed in a caucus on their own substitute for a plan by Sen. William V. Roth (R-Del.) to require Congress to hold spending to within 21 percent of the gross national product, a GOP idea that many of them feared to oppose.

The proposal, which the majority Democrats will seek to push through when the Roth measure comes up next week, calls for the Senate Budget Committee to propose a balanced budget for fiscal 1981 and report out a companion amendment containing enough cuts to meet Roth's 21 percent target.

Budget Committee Chairman Edmund S. Muskie of Maine told the caucus that achieving Roth's goal would require slashing spending by $45 billion and "throw the country into havoc."

The new budget resolution also calls for measures to strengthen the five-year-old congressional budget process, first by requiring legislative committees to make recommended program cuts and then by allowing House leaders to hold budget-busting bills on the desk rather than sending them to the president for his signature.

The House liberals who opposed the resolution yesterday included Stokes, Obey, Paul Simon (D-Ill.), Stephen J. Solarz (D-N.Y.) and Elizabeth Holtzman (D-N.Y.).