I'm not sure why you have to walk your bike. I have had several broken spokes over 32 years of riding and never had to cut a ride short. Just open up the brake calipers if that is where the wheel is rubbing. You can do that with the quick release, or if you need more room, just loosen the cable and let the brakes open to full width. Be careful regarding speed and traffic however. You won't have any braking to speak of on that wheel.

If the rubbing is on a chain stay, use a spoke wrench (do carry one!) to loosen the opposite spokes near the break and tighten the spokes nearby on the same side as the break. It doesn't have to be anywhere near perfect. That should provide enough clearance to get in a good ride and should allow you to close you brakes up enough to have some braking in both wheels.