Not too clear on the exact timeline myself, but wasn't Rick on a drip? They should have kept him hydrated for a least a while. Not long mind, but enough I think to allow him to last about a week on his own. IIRC you can go a *long* time between meals and live, but three days is about as long as you can go without water.
Actually, come to think of it, aren't coma patients supposed to be put on nutritional IV as well as just fluid replacement?
Of course Rick spent the whole time in bed, not moving and thus not burning many calories. So even assuming he used up his IV bags, while he would have been pretty weak and thirsty when he awoke, I think it's within the realms of possibility.