The Bugatti Veyron tires would fail after 15 minutes driving at 400 km/h+
Although the fuel tank will be empty sooner than that, the tires seem to be the weak link.
Will spraying fine water droplets cool tires enough to go beyond 500 km/h?
Increasing the Tire Life Span by Means of Water Cooling
http://eprints2.utem.edu.my/8585/1/IJMM ... terjet.pdf
Would sprayed water cause some aquaplanning or dangerously reduce friction at such high speeds?
Land speed tires are made of very hard rubber compounds that already have low friction so maybe friction won't be an issue at all.