The Senate yesterday emphatically overrode President Carter's veto and killed his oil import fee, handing him his most humiliating defeast so far on Capitol Hill.

The vote was 68 to 10, far more than the two-thirds necessary to override a veto. The House overrode the veto Thursday night by an even bigger majority, 335 to 34 -- meaning that the dime-a-gallon gasoline fee is dead.

It was the first time in nearly three decades that a Democratic president has been overridden by Congress under either Democratic or Republican control. The embarrassment was compounded by the fact that the blow was inflicted by a vast majority of Democrats as well as Republicans, just days after Carter won enough delegate votes for his party's nomination for a second term.

The administration yesterday indicated it was in no hurry to propose an alternative energy conservation measure, although the White House has been considering removal of price controls on gasoline or a speed-up in the decontrol of crude oil prices now under way. "We'll just go about hammering out our policy," said Treasury Secretary G. William Miller.

Faced with imminent meetings of both the Organization of Petroleum Exporting Countries and of oil-consuming nations, Carter lobbied hard for the fee, in part to demonstrate his determination to curb American energy consumption. But he also demonstrated, perhaps even more vividly, his lack of influence on Congress. The leaders went along, but the troops rebelled.

Leading what he characterized in advance as a lost cause, Senate Majority Leader Robert C. Byrd (D-W. Va.) said Carter had "not done a good job" selling his proposal. But Byrd defended it as a "modest attempt to reduce gasoline consumption." The Senate, he added, "may bury the oil import fee but it will not bury this urgent national problem" of dependence on oil imports.

Others, however, were scathing in their denunciation of both the fee and Carter's suggestion Thursday in his veto message that Congress was bowing to political self-interest in vetoing the fee.

"It makes no economic sense, it makes no social sense, it makes no energy sense," said Sen. Dale Bumpers (D-Ark.), adding derisively that Carter "has the courage to say this body doesn't have the courage to vote for this nonsensical proposal."

"It discriminates against those who must drive," said Senate Minority Leader Howard H. Baker Jr. (R-Tenn.). "I think, in a word, it is unfair."

Carter imposed the fee in March both as an energy conservation tool and as a cushion for his proposed balanced budget, but its implementation last month was blocked by a federal court order that has been appealed by the administration. It would have raised $10 billion to $12 billion annually through a 10-cents-a-gallon surcharge on the pump price of gasoline.

Although Carter's action did not require congressional assent, prompting him to claim he was shielding Congress from the political repercussions, Congress was demonstrably eager to share in the election-year political capital of killing it.

"Congress should be ashamed," said Sen. Gary Hart (D-Colo.), one of the fee's few defenders.

Carter lost six votes from the Senate's earlier 73-to-16 vote to kill the fee. Sen. Sam Nunn (D-Ga.), who switched to the anti-fee side yesterday, said he would have stuck by Carter if the president had proposed to use the new revenue for a tax cut. Sen. Edward M. Kennedy (D-Mass.), Carter's challenger for the Democratic nomination, voted to override, as did most powerful Senate committee chairmen. All Washington-area House and Senate members supported the veto override.

The override served to extend the debt ceiling -- and thereby the government's power to borrow money to pay its bills -- until June 30. Foes of the fee succeeded in linking the two measures to gain added leverage for killing the fee. The Treasury Department immediately announced it was resuming the sale of bonds, which it suspended Thursday night when the debt ceiling expired.

The override also apparently ended litigation over legality of the fee. "From our perspective, the ballgame's over," said Jack Blum, an attorney for the congressmen and others who challenged the fee.

Raising energy prices to discourage consumption has been a key part of Carter's energy program, and Congress has rejected several other energy-related revenue proposals, although never quite so dramatically. While Republican presidents often have had vetoes overridden by Democratic Congresses, no Democratic president has been overridden since Harry S. Truman tried unsuccessfully to veto the Walter-McCarran Immigration Act in 1952. Until this week, Carter had successfully vetoed 21 bills.