I'll probably take it in sometime today, but I didn't even realize the extent of the problem until it just happened on the front wheel a few days ago. Then I compared it to a neighbors bike, and saw how big the difference in clearance was. Originally I flatted a few times on the back tire because of this and thought it was just a normal flat. Then I was staying up in WI for a few days cycling when I needed a new tire. The LBS there figured out what the problem was. Until then I didn't even realize such a thing would happen especially on a new bike(sounds dumb in hindsight).
I got a new tire and carefully aligned the pads and wheel, and nothing has happened on the rear since. I think this is mostly because the rear brake pad is worn away at the area where it'll come into contact with the tires from the previous times it made contact. Put a new pad in there and you'll have the same problem. Until I get longer calipers I don't feel comfortable cycling on this bike.