It's been tried a few times... Probably the best challenge was the USFL, but they couldn't make a go of it over the long term, and that was when the NFL media machine was much less entrenched. The ESPN 30 for 30 film "Small Potatoes: Who Killed The USFL?" is pretty interesting (especially given that Trump was a key player in that drama)[1]
[1] http://espn.go.com/30for30/film?page=small-potatoes-who-kill...