Tires are a touchy subject and advice is hard to give when speaking of tires. Personally I would not worry about 60 miles just take it easy and double check tires along your way and keep your speed down. Blow outs are always a possibility though depending on actually tire condition. Gone Busing has made a valid point with AAA. To my knowledge AAA will tow 100 miles free of charge as long as you're a AAA RV Plus Member.
AAA Plus RV or AAA Premier RV Membership