NEW ORLEANS — The lawmakers filled a room near the Florida State Capitol before lunch on Monday, around the time Clemson and Louisiana State football players received their wake-up calls on the morning of the national championship game.

But for all of the frenzy in New Orleans, the site of Monday night’s game, the legislators had gathered in Tallahassee to study an issue with far broader repercussions than the crowning of one season’s champion: whether states should try to force the National Collegiate Athletic Association to allow college athletes to profit from their fame.

There are more meetings to come: During the most lucrative time of year for college sports, from the day of the football championship through the basketball bonanza known as March Madness, and beyond, lawmakers are poised to have the N.C.A.A.’s principles and policies under siege in legislative sessions from coast to coast.

The debates that are expected in more than two dozen states — including Florida, Georgia, Minnesota, New York, Pennsylvania, South Carolina and Washington — could accelerate political and legal reckonings for the generations-old notion that college athletes should not be able to profit from their names, images or likenesses, a philosophy that has largely held as billions of dollars have flowed through the N.C.A.A. and its member schools. The matter also extends to the nation’s capital, where more lawmakers are scrutinizing the N.C.A.A. and signaling that Congress could intervene.