Riding with only one brake: unwise.
Riding with only a rear brake: really unwise. The majority of your stopping power comes from the front wheel. Without a front brake, you can't stop anything like as effectively. Using just a rear brake may be ok for low-speed pottering around, but not for anything else. Replacing a cable is such a simple job there's really no excuse for not repairing the front brake. Use alternative transport, and stop by a LBS on the way home for a new cable. In a pinch, you could remove the rear brake cable and use it on the front in order to get to the bike shop.