I don't know if the Colts are built to stop the short passing game. They are a small, fast, agressive defense. Small, fast, agressive defenses are suseptable to screens and slants because they can overpursue.
The Tampa 2 is designed to allow the short plays, but not allow big plays. The safeties usually play the field deeper on passing plays to keep the play in front of them. In fact, I will argue the Colts Tampa 2 is built for the Pats to go to the short passing game.
I enjoy your posts, and think that you are quite knowledgable, however I respectfully disagree here on a few points.
1) I think that we need to define the Colts D a little better. Yes, they are undersized and quite fast. What they are not, is agressive. Rex Ryan D's are agressive. Jim Johnson's defenses were agressive. Wade Phillips defenses were agressive. While the Colts are a single gap defense, they are not agressive. In fact, with the exception of the pinching slant play they ran during their championship run, they are very much so a reactionary defense. They're just exceptionally fast so they look agressive.
2) If you're good at the screen game (and NE is the best team in football at running screens) you can pretty much screen anyone. However, the NE bread and butter perimeter screens are blown up by pursuit. Specifically, lateral pursuit. No matter what defense you run, the screen is going to put hats on the intitial players. The arriving pursuit is what dictates how far the play is going to go (assuming a backer, safety or corner doesn't make an exceptional play). With the team speed they have, the screen game will be swarmed quickly.
3) The concept of the cover-2 is to remove the deeper stuff as well as the mid to deep crossing routes/seam stuff. However, if you are going to conceptually remove the deeper stuff, you need to build a unit under it that is world class in pursuit. Defenses aren't designed to have simple weaknesses in them, and just because it is avertised to be a big play stopper, does not mean that it is incomplete. It's a get off the field defense, and accordingly is not designed to allow an offense to pass for 4-6 yards everytime they drop back.
4) The defense is a pass defense. This is understood both by the primary coverage designations, and by the players needed to execute the scheme. The problem with the cover 2 stuff is that you need very specific players to execute the defense. Players who simply are too small to effectively defend against the run. Specifically, the linear, directional run game. These guys are highly disciplined, and their speed enables them to recover quite well from the occasional overpursuit. You have to line up and attack the Colts head on, force them through run game attrition to bring the safeties down, then exploit the over route and hope for a clean release. Against these defenses, you need to force them to adjust outside of their normal comfort level, anticipate the call, and catch them for the quick strike when the opportunity presents itself.