That would depend on how fast you are driving.
Every state in the U.S. has a different average speed limit. The fastest is in Texas which is 78 mph. While Alaska's average is 55 mph. Using the time=distance/speed formula, in Texas it will take you a little over than 128 hours or more than 5 days to achieve 10,000 miles.
If you are driving a Formula 1 car (the fastest lap recorded was an average speed of 162.95 mph) it will only take you 61 hours or 2 and a half days.
The fastest qualifying record for NASCAR is 212.80 mph. So if you’re driving this type of car, it would take you about 47 hours or less than 2 days.
If by any chance you are driving Thrust SSC, which holds the fastest land-based vehicle record of 771 mph, it will only take you around 13 hours to reach 10,000 miles.
Check out the 20 Fastest Land-Based Vehicles ever from Cheat Sheet.