There are a bunch of places on the Lower East Side. The Express Tailor on Rivington recently hemmed three pairs of pants for me in 15 minutes and their prices for routine alterations are totally reasonable (I think $5 to hem a pair of pants). It's a bit of a schlep from Times Square, but there are plenty of good eats within a couple blocks to justify dropping your stuff off before lunch and picking them back up after.

For something closer, my friends in Chelsea used to swear by Wilfred's Tailoring (http://www.wilfredstailor.com), although I'm not sure if they still use them or not, and I don't know if they do same-day or not. But you might try giving them a call.