Cannonball run is 2906 miles. Assuming most of it is across highways at 65 mph, (a lot of the west is faster but the east is slower), you'd get it in about 44 hours. With a 10-minute delay every 300 miles you'd add about 2 hours for a total of 46.3 hours.
You want to stop every 16 hours of driving (since you don't care about DOTs 10-hour limit) so it takes you slightly less than 3 days. Or less than half the stated "week".
This is unfortunately why this will never happen. It's 4x as long as flying and requires 1000x the infrastructure to maintain. High speed rail makes sense for regional connections, but I remain skeptical that it's viable for this kind of travel.
I mean, any network is just a set of regional connections. Sure maybe no one takes NYC - LA line, but if people are taking the NYC to Chicago and LA to Dallas and Dallas To Chicago there's no reason not to join them up.