Being that this is such a special event/location, I'm not sure this will be true, but i have never had a problem getting colts/pats tickets. Even in the manning/brady heyday years I could show up at the stadium and wait at the will call for seats to become available. I was told that the players are distributed tickets (I stat behind Brady's sisters once) or people find out at the last minute that they cannot use their tickets and often will call them in to be sold by the stadium and that was why they trickle in and become available just hours before the game.
It's not the best option and there is certain risk, but the benefit may outweigh that risk.