This would entail making Brohm one of the 45 active players for the game, then you can play whoever you want. The rule is designed to allow a 46th player to be eligible but only for emergencies. Also the rule has apparently been updated to allow the emergency quarterback to play in the fourth quarter and still have re entry of one of the active quarterbacks
The rule, from the NFL:
"Teams will be permitted an Active List of 45 players and an Inactive List of eight players for each regular-season and postseason game. Provided that a club has two quarterbacks on its 45-player Active List, a third quarterback from its Inactive List is permitted to dress for the game, but if he enters the game during the first three quarters, the other two quarterbacks are thereafter prohibited from playing."
The third quarterback is the 46th player, so you don't have to waste a 45th spot on a guy who will, in all likelihood, never play. It used to be if the third guy went in anytime, the other two couldn't play, but they changed it a few years back.
Basically, the third guy is for an emergency. And keeping the other two guys from playing makes sure you keep his use to emergency situations.