Standard atmospheric pressure at sea-level Earth is just 14.696 psi. Compare that to 340 or 300 psi (23.14 and 20.42 amt, respectively). The difference in internal tire pressure in Earth's atmosphere and absence of atmospheric pressure in vacuum of space is only 4.3 - 4.9%. read more
According to the NASA specifications on the space shuttle tire: It is designed to withstand impact landing of 263 mph of a vehicle weighing 142,000 pounds. It is a 34 Ply tire, nominally inflated to 340 PSI. read more
The difference in internal tire pressure in Earth's atmosphere and absence of atmospheric pressure in vacuum of space is only 4.3 - 4.9%. Tires would experience far more dynamic pressure environment due to friction heating and pressure of weight of the orbiter during landing (240,000 lbs / 109,000 kg) at contact speeds up to 260 mph (418 km/h) than those ~ 5%. read more