The reality is that the Government can try to establish as many "pay for play" rules as they want and the Conferences can lineup to adopt them...
But all of that is completely irrelevant if there isn't a highly punitive, brutally strong, enforcement mechanism put in place to ensure that the individuals colleges, coaches and players are following the rules. The NCAA has no teeth and colleges have simply realized that they can threaten to sue, and get their way as a result, despite being in the wrong.
Unless there is a national commisioner put into place, with agreed upon powers (and a substantial budget) to enforce rules, any administrative attempts by Congress will be worthless.
Alternatively, the only other way to get the schools to back down is to have NCAA legal matters be handled by the DOJ, so that they have an unlimited budget (the taxpayers purse) to counter sue universities out of existence that try to use the threat of lawsuit to escape justice... And let's be real, nobody really wants this. That sounds like an area I don't want the Government involved in.
Wake me up not when there are rules put into place, but when there is a sufficient enforcement mechanism put into place to absolutely curb stomp any individual or university caught cheating.