About three months ago, John P. Philbin, chief lobbyist for the Mobil Oil Company, was watching television with his two daughters in their Arlington town house. There on the screen was President Carter, blasting the oil companies for keeping profits he said they had not earned.

"Don't let it bother you," said his older daughter, "We still love you."

"Yeah," added the other. "We think you're still a good American."

It was a rare compliment for Philbin, whose job may be the most unpopular in town. As a lobbyist for one of the country's major oil companies, he is often perceived as a backroom operator cooking up secret agreements with congressmen, that result in higher gasoline prices.

Not so, he says. "You can't buttonhole them anymore. They resent it. There's nothing to be gained."

Instead, Philbin and his associates make only occasional trips to the Capitol for scheduled appointments. And he carefully observes the Hill's pecking order, nothing that "if you run into the boss without first seeing his staff, they'll cut your throat."

Philbin, with 25 years of experience in the lobbying trade, says he never directly asks a congressman for a vote. "I say 'This is the result. I think this is what you are seeking to do. I think it will accomplish this.' Naturally, if i'm opposed to the bill, i'll stress the negative aspects of the result."

Once last year, Philbin took a a top Mobil executive to a congressman's office for an appointment that had been scheduled well in advance. They sat for 40 minutes as the congressman chatted on the phone with a grocery store owner back home. Finally, the oil-men were given an audience, for all of five minutes," muttered Philbin to his chagrined boss.

Philbin rides the subway to work, but recently he took his '79 Chrysler LeBaron to the gasoline station, where he waited in line with everyone else. It was not a Mobil station. Philbin says je and his wife never fill up at a Mobil station, lest someone discover who they are and complain that they are getting special treatment. CAPTION: Picture, no caption, By John McDonnell - The Washington Post