Very competitive space but you don't have to be a genius to know how to move product. The paradox lies within what SniperRyan said, though...
You don't want to make the same shirt that everyone else has already made. And profit margins on tshirt sales are very slim. So what you're doing is putting a product out there that, by design, will appeal only to a specific group... but you are dealing with advertising technology that cannot target to that level.
Sure you can come very close... Facebook targeting and funny news sites and shit like that. But my point is that the thinner your margins are, the more every centimeter of that target starts to matter. Sure you can make a funny slogan, give out some shirts, and wait for someone to see one and go home to google it... but is that kind of volume the big payday you're working towards?
You have to figure out if you're trying to sell funny tshirts or brand a funny tshirt company, because there's a big difference.
If I were going to do it, I'd select 3 groups that I knew I could reach with no guesswork, and who I thought were anxious to wear their hearts on their sleeves, and make shirts tailored (no pun intended) to them.
So for example...
Group 1: Hardcore conservatives
Group 2: "Child-free" advocates
Group 3: Anti-Scientologists
Measure which perfroms best in terms of cost per sale, volume and repeat business. Then analyze the market surrounding it and expand in that line. Political? Activist? Edgy? Misanthropic?
Just food for thought.