When President Reagan signs the Surface Transportation Assistance Act of 1982, the first thing consumers should notice is that tires for their automobiles will be a little cheaper.

That is because the act, known variously as the nickel-a-gallon gasoline tax increase or the highway repair jobs program, repeals immediately a federal excise tax that adds between $1.50 and $2.50 to the cost of a car tire.

The nickel increase on gasoline and diesel fuel will take effect April 1 and will be imposed at the refinery.

Because gasoline prices have been dropping slowly in what economists call a "soft market," drivers may not feel the full impact of the tax increase.

"You can predict in the long run there will be a sharing of the tax by consumers and producers," Milton Russell of Resources for the Future said, but he added it was impossible to predict what that will be on April 1.

Other features of the four-year act are read either as victories, losses or ties by interests as diverse as highway contractors, truckers and mass transit operators.

"This is a tremendous move forward," said Transportation Secretary Drew Lewis, who had led the charge for the tax increase, first in the administration and then on Capitol Hill.

"It is particularly a breakthrough for mass transit," he said. But he also cited the need to rebuild crumbling highways and bridges which, he said, have been ignored for 15 years.

The truckers claim they have lost because of a major increase in heavy truck use fees, which they claim will cost them more than $2,200 for a typical 18-wheeler in 1985. But those increased taxes will not begin to be imposed for 18 months, which gives the trucking lobby time to seek relief in Congress.

It also will be a while before automobile drivers have to start dodging the wider, longer trucks with double trailers that the act permits truckers nationwide. But the law, written in a hurry, permits wider trucks immediately and heavier trucks 90 days after enactment.

"That will wipe out the trailer manufacturing business," said Bennett C. Whitlock Jr., president of the American Trucking Associations and vocal leader of the opposition to the truck taxes.

"That's more trucking bull," said a Transportation Department official who asked not to be identified. "Obviously we have to fix that little problem administratively, and we will."

Francis B. Francois, executive director of the American Association of State Highway and Transportation Officials, said he thinks it will "be some time" before two-trailer rigs are widely used in the District of Columbia and 14 eastern states including Virginia where they are banned today.

"The wider trailers may come sooner than the double trucks," Francois said. "The problem is the equipment change. If the trucking industry is anywhere near the fiscal straits it claims to be in, it will be some time" before new equipment is on the road.

Whitlock made the same point. The average truck trailer, he said, lasts for 15 years and "even the large companies can't afford to turn over a trailer that has six or seven years of life left in it." He conceded that large trucking companies will be in a better position to take advantage of the larger size limits than the small independents.

The reason mass transit is such a big winner is because, for the first time, it has a guaranteed source of federal revenue and the right to spend it, just as the highway people have had since the beginning of the highway trust fund in 1956.

Transit will get 1 cent of the 5-cent-a-gallon increase, and that money will be maintained in a separate account within the trust fund.

"This bill gives us four years of stability and certainty," Jack R. Gilstrap, executive vice president of the American Public Transit Association, said.

"For the first time ever we have a dedicated source of funding . . . . This will permit transit planners to have some certainty that funds will be available for those major porjects which span many years."

But the biggest winners, without question, are state highway departments that have watched their federal aid steadily dwindle in practical terms since 1959, the last time the gasoline tax was raised.

Francois' group, which represents almost all state highway departments, estimates that between $5 billion and $6 billion in road and bridge work can be put out for bids within 90 to 120 days.

"Two factors concern us," Francois said. "One is the impact this money will have on the construction cost index; how much work will it buy. The second is the availability of contractors and materials."

John Berard, a spokesman for Associated General Contractors, said "I don't think there's any danger in not having enough contractors around to do the work; our contractors are waiting and ready and capable."

H.C. Heldenfels, president of the contractors' group, said that because of the act, "hundreds of thousands of unemployed construction workers and construction equipment manufacturer workers will soon be going back to productive work."