The thorniest issue facing Congress this year won't necessarily be what to do about the deficit, arms control or the Nicaraguan "contras." It may be what to do about the Raiders, the Colts and the Eagles.

With a growing number of professional sports teams abandoning their home cities or threatening to seek greener pastures, Congress will consider at least five major bills to tackle the problem. They range from giving the National Football League more authority to control franchise shifts to blocking all major-league teams from moving without government approval.

The most far-reaching measure, the Professional Sports Team Community Protection Act, would have the Commerce Department set up an arbitraton panel to regulate franchise shifts in baseball, football, basketball and hockey. A team would have to demonstrate that it had an inadequate stadium and had been losing money for several years.

The bill, to be introduced next week by Sen. Slade Gorton (R-Wash.) and several colleagues, has an added twist. It would require pro baseball to expand by two teams and pro football by four, two of which would be mandated for Baltimore and Oakland.

"Everyone who represents a city that has a franchise favors this," Gorton said. "But every member who represents Phoenix or Louisville and wants to get a franchise is hurt by stability, because there's no longer a city they can raid . . . . We're giving those cities a crack at it."

Skeptics, however, say that pressure may build to award franchises to all 435 congressional districts. Sen. Frank R. Lautenberg (D-N.J.), whose state is looking for a baseball team, said last year, "The basic problem is that there are not enough teams to go around . . . . A community that wants a team, that can field a team and that can support a team should have a team."

The major sports leagues have mounted a strong defense against some of the legislation, although the NFL favors legislation to allow the league to make the decisions.

"These are essentially business judgments," said attorney Paul Tagliabue of Covington & Burling, one of several Washington lawyers who represent the NFL. "We just don't want Congress telling us" where teams can play.

One sports attorney said owners who are determined to move will find a way around congressional rules. Still, many lawmakers are angry that teams playing to sellout crowds are leaving in search of still greater profits.

Congress also is under pressure from have-not communities looking for major-league sports to spur economic development. Cities from Buffalo to Tampa are spending as much as $80 million on baseball stadiums in hopes that a new team will boost tourism and improve their images.

The latest franchise shifts began when Al Davis defied the NFL and moved his Oakland Raiders to Los Angeles in 1982. The NFL sued, but a federal appeals court hit the league with a $50 million judgment, saying it had violated antitrust laws by requiring that three-quarters of the club-owners approve any relocation.

The ruling turned the league into an idle spectator while Robert Irsay moved the Baltimore Colts to Indianapolis. City officials, not the NFL, persuaded the Philadelphia Eagles not to leave for Phoenix. It wasn't long before Sens. Pete Wilson (R-Calif.), Charles McC. Mathias Jr. (R-Md.) and Arlen Specter (R-Pa.) became increasingly interested in the issue.

Specter has introduced a bill that would force the NFL to restrict franchise shifts and to repay Philadelphia for the $30 million the city had to spend to keep the Eagles.

Sen. Dennis DeConcini (D-Ariz.) plans another bill that would give the NFL an antitrust exemption to stop its teams from moving. While Phoenix failed to snare the Eagles, DeConcini said, "If you're trying to get a team, you'd like some protection that they won't move off to Salt Lake City or Albuquerque because someone promises them a better skybox."

DeConcini can afford a limited approach because Phoenix is in line for a football team if the NFL expands. And NFL officials have let it be known that they will add teams if they can regain the power to control their franchises.

Congressional staff members point out that football expansion has followed every major bill passed by Congress for the NFL: a 1961 antitrust exemption for teams to pool television revenue; the 1966 approval of a merger with the American Football League and the 1973 lifting of television blackouts on home games.

NFL Commissioner Pete Rozelle made the connection in Senate testimony last year. "I personally and the other owners in the league feel a responsibility, when Congress passes something for you, to give a quid pro quo to show a sense of responsibility for that action," he said.

James Fitzpatrick, an attorney for major-league baseball, said there is no reason for any bill to include baseball, which has enjoyed total antitrust immunity for decades. He said there have been no franchise shifts in the last 10 years and that every city that once had baseball now has a team, with the exception of Washington.

But reports that the Minnesota Twins, Pittsburgh Pirates and other clubs may move elsewhere have many lawmakers worried that they too may be left with empty stadiums and angry fans. This has prompted several bills on the House side as well.

The National Basketball Association is grappling with the same dilemma, having sued the San Diego Clippers for moving to Los Angeles last year without the league's approval. Nevertheless, said NBA attorney Philip Hochberg, "I'm not sure that legislation is necessarily the best answer."

Gorton said Congress has a right to regulate big-league sports because it has granted them a near monopoly and because most teams play in stadiums built at public expense, such as Seattle's Kingdome.

As Washington's state attorney general, Gorton sued the American League in 1970 for pulling the ill-fated Pilots out of Seattle after one season. The suit was settled several years later when Seattle was given another team.

"There's probably more interest among members on this than at any time in the past," Gorton said. "Whether that's enough to conquer the opposition of the major sports leagues is dubious.