By mid-afternoon Thursday the lobbyist from General Motors had his victory behind him. He could afford the luxury of a catnap in a back row of the House Ways and Means Committee's hearing room.

Across the Capitol, the pace was a bit more frenetic. In the lobby outside the Senate chamber, at one point, former United Auto Workers President Leonard Woodcock was grasping Sen. Hubert H. Humphrey (D-Minn.) by one arm and current UAW President Douglas Fraser was clinging to the other.

The auto industry, labor no less than management, was busy all over Capitol Hill this week. And it did rather well, especially in light of the fact that it was tilting against the President of the United States.

At issue in the House Ways and Means Committee were the automotive provisions of President Carter's energy program, particularly the gas-guzzler tax the White House wanted to start imposing this fall on 1978 model cars.

Under the prodding of the Big Three automakers, Ford, Chrysler and GM, the commitee decided to cut the penalty taxes drastically and to postpone their first imposition until next year, when the 1979 models come rolling off the assembly lines.

"They came a long way in getting out from under any real impact on ultimate sales," said Robert Brandon, a lobbyist for Ralph Nader's Tax Reform Research Group. "By 1985, I figure they're going to be taxing Sherman tanks, and that's about it."

The lobbying coalition arrayed in the Senate to win a delay in automobile-pollution cleanup deadlines (they were supposed to come into play this fall) was even more formidable, although it was somewhat less successful.

According to Senate sources, the President personally put out a distress call Wednesday to Senate Majority Leader Robert C. Byrd (W-Va.). Carter asked him if he could enlist the Democratic leadership and put together the votes to avert the four-year stretch out the auto industry was seeking.

The jockeying produced some interesting convolutions. After an elaborate presentation by Woodcock weeks ago, Sen. Frank Church (D-Idaho) put his support of the UAW's position on paper.

At the showdown Thursday, however, Church voted the other way, supporting a compromise sponsored by Senate Minority Leader Howard H. Baker Jr. (R-Tenn.) and eagerly backed by the administration as the best it could get. The auto industry had been expecting Church to vote for a 1982 deadline sponsored by the two senators from Michigan, Robert P. Griffin (R) and Donald W. Riegle Jr. (D).

Church, however, "doesn't feel he reneged," a spokesman said yesterday. The Idahoan would have favored the auto industry amendment over the strict 1980 deadline sought by Sen. Edmund S. Muskie (D-Maine), the spokesman said, but "he felt the Baker amendment was a reasonable compromise."

But while it lost some, the auto industry also won some.

About an hour or two before the vote, Sen. Charles H. Percy (R-Ill.) was seen by one Senate head-counter having coffee with Woodcock and Fraser. Percy had been counted as uncommitted until yesterday afternoon. He voted with Detroit, which had already won the stretchout it wanted - until 1982 - from the House.

Senate Energy Committee Chairman Henry M. Jackson (D-Wash.) said yesterday the predicted long ago that a united front of auto management and labor could create a "political firestorm" on Capitol Hill.

"They hace tremendous influence," Jackson said."They won in the House [on pollution stretchout] and they almost got away with it in the Senate." A UAW lobbyist put it more contentedly: "We're doing pretty good. We got a full loaf in one house and half a loaf in the other and we've still got a [Senate-House] conference ahead of us."

The skirmishing in the House Ways and Means Committee was much easier for the automakers.

President Carter has called his energy program "the moral equivalent of war," but Ford, Chrysler and GM lobbyists didn't even have to work up a sweat over Carter's standby gasoline tax and his proposed rebate for high-mileage cars.

"The members [of Ways and Means] made clear there wasn't much sentiment [for those proposals]," said Ford's Wayne Smithey. As for the campaigning agaisnt the President's gas-guzzler tax. Smithey said, "I'd hardly characterize it as a big effort."

"The UAW wasn't even busy there," said Nederite lobbyist Brandon. "They let industry do almost all the lobbying with Ways and Means. That's interesting because usually they're pretty uncomfortable lefting industry run the show."

Ford representatives complained that Carter's guzzler tax would put them at a competitive disadvantage with GM. According to the Ford lobbyist, only a few committee members twitted him about the company's advertising of the past year, proclaiming it dedication to "the full-sized car." It was only last fall that Ford President Lee Iacocca happily quipped: "The difference between our cars and GM's is the difference between a four-foot blonde and a seven-foot brunette."

The mark-up session in Ways and Means was laced with denunciations of Detroit as selfish, duplicitous, monopolistic and worse, but there were very few votes to back up the rhetoric. When one congressman labeled the automakers "their own worst enermies" and then voted for them, Rep. Otis G. Pike (D-N.Y.) shot back:

"They may be their own worst enemies, but we are their own best friends."