I was doing a little napkin-math to see what my power/space constraints would be.
Reading the specs of the CR2032 battery, I found that the maximum rated continuous current is 1mA and the max pulse current is 10mA. Typical full-size LEDs take something like 20mA. But even if the LEDs only took 5mA, that's too much when you factor in all the other crap on the watch.
I'm not too worried about it at the moment though. I'm assuming I can push the battery a little because I won't be drawing boatloads of current out of it continuously. I took the back off my binary watch and found that its massively bright bank of LEDs runs off a CR2032 and it might have up to 8 LEDs on at a time.
As far as space constraints go, I'm glad to see that surface mount LEDs are so diverse. Metric package sizes are usually listed by length and width as measured in mm. For example, a 1206 is 1.2mm by .6mm. My watch face is about the size of a gold dollar coin or 26.5mm across. That gives me an outer circimference of 8.32cm or around 1.4mm per LED. Seeing how I can pack LEDs very very close together, I should have no issues if I pick packages like an 0402 (that's as small as I could find).
My other main concern is brightness. Most of the LEDs I've been looking at are around 5-10mcd, but I have no way to judge exactly how bright that will be. I suppose I'll have to worry about that later.