When William A. Meehan, lobbyist, marched into the office of Sen. Arlen Specter (R-Pa.) one day last month, no round of introductions was necessary.

Meehan does not cut much of a swath in Washington; he's never lobbied here before. But in Specter's home town of Philadelphia, Meehan has been the Republican Party boss for the past two decades, and he's the closest thing Specter has to a political godfather.

His lobbying visit was financed by the Milliken Research Co., a South Carolina-based textile firm found guilty of price fixing in a bitterly contested 12-year-old antitrust suit.

Milliken is trying to persuade Congress to rewrite the antitrust laws and apply the changes retroactively to its case, thereby reducing by two-thirds the potential damage judgment of $21 million it faces.

It already has retained two South Carolina lawyers and a third from Washington to help it lobby the bill. But with so much on the line, the firm has now moved on to hiring what practitioners of the trade describe as specialty or "bullet" lobbyists, whose sole function is to line up the support of a single legislator.

Meehan's quarry is Specter, a potential swing member of the Judiciary Committee, which is expected to vote on the bill within a week. "He's the only one on the committee I've approached because he's the only one I know," the Philadelphian explained.

Hiring an out-of-town counsel for that sort of one-on-one lobbying is an uncommon indulgence, but Milliken and a handful of other companies (including Mead Corp., Georgia-Pacific Corp., and Weyerhaeuser) that lost different price-fixing cases are sparing no expense in behalf of S. 995.

The cast of lobbyists on the bill, dubbed the "Price Fixers Relief Act" by its opponents, is a diamond-studded assemblage of former senators, ex-Cabinet members, Washington superlawyers, and corporate brass.

Senators on the committee say privately that they have never seen such a collection of talent, time, and money brought to bear on so narrow an issue. The fight is not over whether the antitrust laws should be changed (most members of the committee agree they should be), but whether the changes should apply prospectively only, or retroactively as well. For a handful of big companies facing damage awards in pending cases, tens of millions of dollars are on the line.

"Arlen told me there had never been a more heavily lobbied special interest bill in the Senate in the last 20 years," said Meehan, with hint of pride at having been called in on such a high-stakes case.

If he needed more confirmation of the dimension of the lobbying effort, Philadelphia's "Mr. Republican" found it when he showed up at a Judiciary Committee hearing last month.

Not too many senators were on hand to listen to the arguments on retroactivity (they had by then heard them dozens of times in private meetings), but in the back of the room were almost enough ex-Judiciary Committee members to provide a quorum.

There, quarterbacking the presentations for the firms seeking retroactivity was former attorney general Griffin B. Bell. His lead witness was former senator Sam J. Ervin Jr. (D-N.C.), and his lead behind-the-scenes operative was former senator Birch Bayh (D-Ind.), an original author of the bill, who was working the halls outside.

Not in the room that day, but lending a hand to the retroactivity forces at other points along the way, were former attorney general Benjamin R. Civiletti, former solicitor general Robert H. Bork and superlobbyist Charls E. Walker.

The opponents of retroactivity had not exactly fielded a slate of slouches, either. Their effort, which came complete with its own public relations firm, was led by former senator Joseph Tydings (D-Md.), former senator Robert P. Griffin (R-Mich.), Carter administration adviser Stuart Eizenstat, Vice President Mondale's chief of staff Richard Moe, and constitutional scholar Charles Alan Wright of Texas.

The Judiciary Committee has been getting its ear bent by these gentlemen, and a supporting cast of 40 or so other lawyers, for nearly a year. "I'm about to the point where I want to knock heads," said Sen. Howell Heflin (R-Ala.), a former judge who, along with Committee Chairman Strom Thurmond (R-S.C.), has been urging the disputants to come up with an out-of-Congress settlement.

Various efforts have been made in the past year to come up with creative wording on the retroactivity issue that would satisfy both sides, but so far to no avail. Last week, Thurmond drafted some compromise language, which said in effect that the changes could apply to pending cases if the defendants could show it was inequitable not to have them apply. Nobody quite knows what that means, though, and it seems unlikely to break the deadlock.

Passions are high. Companies that have been fighting each other in court for a decade or more now see the potential fruits of their victory, or the cost of their defeats, undone by Congress.

The victors in the court battles are beside themselves at the prospect of retroactivity. "This is the most blatant form of special interest legislation," writes David Foster, an attorney for Burlington Industries Inc., which won the price-fixing case against Milliken. If retroactivity passes, he continued, "Milliken will have succeeded in getting the rules changed after the game is over because it did not like the outcome."

The other side is no less livid. It claims the laws and tactics the plaintiffs used to win their damage awards were "legally and morally reprehensible" (Ervin) and that it would be a "cruel irony" (Bell) to change them but not permit the victims, price-fixers though they may be, to take advantage of the cure.

Back and forth they go. The vote has been delayed three times in the committee, largely, it is said, because Thurmond is deferring to Milliken, his home-state company, which has been fighting an uphill battle to put together the votes for retroactivity.

Whether it has them or not is problematic. Not too many senators have taken a public position. Specter hasn't either, but he is leaning. Despite the hearings he has given to Meehan and 23 other lobbyists on the issue, he says he is leaning against retroactivity.