America's truckers, one of the best-financed and strongest interest groups on Capitol Hill, are already pressing Congress for relief from the major tax increase on heavy trucks voted last month along with the increase in the federal gasoline tax.

Early betting is that the truckers may succeed, at least partially. "Every congressman in the country has at least one trucking company in his district or has a commodity that needs to be hauled by a trucker," a congressional staff member said. "They can touch everyone."

The American Trucking Associations' political action committee paid out $285,565 to 398 congressional candidates during the last campaign. More than one-fifth of that total--$59,860--was given to members of the House Ways and Means and Senate Finance committees, the tax-writing bodies on Capitol Hill.

So what did it buy?

"I'm not so naive to believe that political contributions do any more than give you an opportunity to sit down with the congressman or his staff members and explain your position," said Bennett C. Whitlock Jr., president of the ATA.

Rep. James J. Howard (D-N.J.), chairman of the House Public Works Committee, which wrote all but the tax section of the House version of the highway bill, received $6,000 from ATA's PAC in the last two years, according to Federal Election Commission records.

He nevertheless voted for the bill, including the taxes, on every occasion it came up in the House.

So did Rep. Dan Rostenkowski (D-Ill.), chairman of Ways and Means, who received $2,020 from ATA.

Sen. Robert J. Dole (R-Kan.), chairman of the Senate Finance Committee, who also voted aye, received $1,000 from ATA in 1979 and 1980, but was not up for reelection last year and got nothing.

On the other hand, Sen. Robert C. Byrd (D-W.Va.), the Senate minority leader, who voted against the highway bill and tax increase, got $9,040, more than any other senator.

It was no secret at the time of the last congressional campaign that trucking taxes were likely to be discussed by the new Congress. What surprised the ATA was the fact that the subject came up during the lame-duck session of the old Congress when long-dormant highway legislation took on the aura of a jobs program.

"I just think this loss by the ATA is an aberration due to fact there was a tremendous push for a jobs bill and a huge highway and transit bill," Howard said. "It all got wound up in its own momentum."

The highway tax and construction bill, signed this week by President Reagan, would bump the heavy vehicle user fees on 18-wheelers from a maximum of $240 a year to a maximum of $1,900 by 1988 if allowed to take full effect.

That, the truckers say, would be confiscatory, and this time they say they do not intend to be bushwhacked in a short lame-duck session where they have no time to mobilize and fight.

But the lame duck was not a total loss for the truckers. "Considering the odds," said Whitlock in an interview this week, "I feel we did a fairly decent job as far as the Hill is concerned."

The Transportation Department, after computing how much damage various kinds of vehicles do to highways and concluding that trucks were not paying their share, initially proposed increasing the heavy truck tax to $2,900 annually, to take effect April 1, the same day the new gasoline tax will take hold.

By the time the administration bill left the Office of Management and Budget the tax was down to $2,700. When it left the House Ways and Means Committee it was $2,000, but would phase in over three years.

When it left the Senate Finance Committee it was $1,600, to phase in over six years. The Senate, by a 96-to-1 vote, cut it to $1,200. The House-Senate conference agreement, which became law, pushed the tax back to $1,900, but the first penny will not be collected until July 1, 1984. It will be fours years after that before the tax reaches the $1,900 maximum.

What was gained in that process was not only a reduction from the administration's goal, but also a substantial amount of time before the tax takes effect.

That time, justified on Capitol Hill as needed to help the ailing industry through hard times, gives the ATA and its allies 18 months to work out a better deal.

The ATA's goal in the new Congress, Whitlock said, will be to reduce the tax at least to a maximum of $1,200 per 18-wheeler.

"I've got to look at the 96-1 vote and figure that is a place to start," Whitlock said. He agreed that the truckers will have to give up something in exchange for liberalized weight and width limits they also received in the new highway legislation.

The Transportation Department says that trucks do 33 percent of the highway damage. Under current tax rates they pay 25.1 percent of the federal cost of building and repairing highways. Under the new tax package, which assumes a much higher level of federal highway spending, they would pay 27.7 percent.

Whitlock's $1,200 maximum would leave them paying 24.6 percent, or less than the current percentage when applied against 1985 highway needs.

Whitlock said, in effect, that the Transportation Department's formulas are all wet, and he has been trying to prove that to Congress.

In years past, the ATA annually held a dinner party at which hundreds of trucking executives would come to visit their representatives.

"It was the best dinner," said Howard. "There were no speeches." One year the cherries jubilee were delivered in small semi-trailer trucks carved from ice and equipped with battery-powered headlights.

The ATA hasn't held that party for several years. "The cost was enormous," said Whitlock. He paused. "Maybe we should do it again," he said, winking.