Not a bad idea, seeing how many companies are taking this approach. Geico's are only marginally related, as does Old Spice. And people remember and talk about them because they're funny - and they associate the brand with it and the brand benefits. Little bit different tack than what, say, Apple does, but if your audience would be receptive to this (i.e. younger adults maybe) then you can be very successful with it.
Looking for something, I would recommend a couple of sources. Twitter's full of people trying to be pithy and clever; dig around, or even post up something asking for contributions. Also, check out some of the places online selling these sorts of t-shirts; go to CafePress.com or BustedTees.com for some good pop culture stuff. There might be some guys out there that would let you put your logo on the back or something. Lastly, go ask some kids, if you can find some, both to ask for ideas and especially to run by for their opinions. They'll tell you straight up whether it's funny or lame (and no one wants their brand associated with something lame).
The news may give you some ideas too. Or some marketing or ad companies might be worth the cost, but you gotta have the cash to do so (and take your chances). The best ad company I know of that's done some real popular ad campaigns is Crispin Porter + Bogusky; go to their website and you'll recognize a bunch of their work (and it's amazing). Or even a stand-up comedian or two, who knows - they may be great for this sort of thing.
Fact is, it's hard to be clever when you're trying to be clever. It's too easy to be cliche, lame, or just forgettable. Good luck with it; I'm curious to see what you come up with. Hope this helps!