1.5-inch tires would do okay. One-inchers would probably be a bit much on cruiser rims.

One-inchers would need to be inflated pretty high--up near 100 PSI--and that's about 30 PSI more than cheaper rims should really be stressed.
Besides, going to one-inchers would drop the drive ratio down a lot (not much mathematically, but it would definitely feed different). Since bicycle tires have basically a round cross-section, narrower tires are also a smaller outer diameter.