The Senate early this morning finally passed its version of the administration-backed highway repair bill that would raise the federal gasoline tax a nickel a gallon.

The Senate leadership had labored for hours to bring the bill to the point of passage over the opposition of a few conservative Republicans. The tax increase -- the last major obstacle to adjournment -- still had to be reconciled with an alternative approved earlier by the House, then be brought back again to the Senate floor.

There were indications this morning that the highway filibusterers might drop their opposition in return for passage of a farm bill, the administration's so-called payment-in-kind plan to curtail production and increase prices. It has already been approved by the House. But some senators were fighting a farm-for-highway trade-off.

While the highway bill lurched forward this way, the House and Senate completed action last night on a long-stalled compromise plan for disposing of high-level nuclear wastes and sent it to the president for his signature. The bill is an effort to solve one of the main problems of nuclear power plants: where to put the extremely toxic spent fuel that is accumulating in storage pools around them. Details, A5.

The leadership was fighting not only the highway bill's opponents but the clock -- a desire in both houses to adjourn for Christmas and until next year with or without action on the gasoline tax, now 4 cents a gallon.

The Senate highway bill differed from the House version not on the gasoline tax, but mainly in how much of an additional tax increase should be levied on heavy trucks. The trucking industry has fought the bill vigorously.

House and Senate leaders and aides held informal conferences all day on these trucking and other provisions, and appeared confident they could work out a compromise.

But the Republican senators who had filibustered the gasoline tax increase for nine days as regressive and wrong-headed in a recession had not given up. Early this morning, even after an 87-to-8 cloture vote, they held the floor in an effort to hold up the bill.

The compromise is expected to be agreed to swiftly when and if it reaches the House, which does not permit extended debates.

The nickel increase, raising the federal tax on gasoline to 9 cents per gallon, would take effect April 1, 1983. Passenger buses, government cars and farm vehicles would be exempt from the tax, as would users of methanol and ethanol fuels. Taxicabs and users of gasohol would pay 5 cents per gallon instead of the full 9 cents.

Since it first surfaced in the weeks after the Nov. 2 election, the real purpose of the gasoline tax-highway bill has been in the eye of the beholder.

Transportation Secretary Drew Lewis and the White House viewed it exclusively as a means of rebuilding the nation's deteriorating roads and bridges.

With the president resisting jobs bills put forward by the Democrats, they could not call it a jobs bill -- and in fact the president's own economist said the tax increase would cost more jobs than the highway repair program would provide.

The Democratic leadership in Congress embraced it as a jobs bill of sorts, although not the one they preferred. Several environmental groups opposed it because it would fund new interstate highway construction, and the trucking lobby grumbled about the levy on heavy trucks.

The House dealt with the measure with relative dispatch, approving it by a 262-to-153 vote in the early morning of Dec. 7. Three days later the Senate took it up, and immediately trouble began.

Four conservative Republicans -- Jesse Helms (N.C.), John P. East (N.C.), Don Nickles (Okla.) and Gordon J. Humphrey (N.H.) -- filibustered against it and frustrated the Senate leadership. More than once the bill's supporters feared it would be talked to death.

Attempts to end the filibuster failed twice last week, forcing Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) to remain in the Senate chamber long into the night, sometimes alone with the wheelchair-bound East, searching for a parliamentary opening he could use to force a vote. East, a senator for only two years, proved a tough adversary for Baker, at one point even arguing that he was not filibustering.

"I refuse to let it be implied that some way or another I am the one who has been dilatory, that I am the one who is obstructing," he said. "I have not said a thing for days around here except in the most limited and appropriate way."

The nickel-a-gallon gasoline tax increase is expected to bring in $5.5 billion a year for highway improvements and mass transit assistance. Four of every 5 cents would go to the Highway Trust Fund for rebuilding roads and bridges and the other cent to a new mass transit fund.

The highway portion would be distributed in such a way that each state would receive at least 85 cents for every dollar its motorists paid.

The mass transit money, however, would be apportioned according to a formula based primarily on need. A last-minute attempt by Sen. Dale Bumpers (D-Ark.) to amend the mass transit section so that states such as his, with few bus systems or subways, would be guaranteed a larger portion was tabled by a 52-to-44 vote.

While the gasoline tax increase is of most interest to the public, it is only one relatively small portion of the highway bill. Several provisions would affect the trucking industry.

Some are to its benefit, such as an increase in the allowable size of trucks on the highways. But the House proposal to increase the taxes to $2,000 for trucks weighing more than 33,000 lbs. impelled the industry to mount a full-scale attack on the whole bill.