How quickly could the entire U.S. population be evacuated?

Completely evacuating the U.S. of everyone in it would probably be impossible, for the reasons noted above. And a lot of people would die in the process, from accidents, road-rage shootings, and even (as the process dragged out, as it inevitably would) disease and starvation.

Including after people crossed the border. Canada and Mexico are set up to look after their current populations, not HUNDREDS OF MILLIONS of refugees.

Are we doing outside the box now?

  1. Develop a cow rabies cure.
  2. Don’t evacuate us, evacuate the cows. City Slickers III writes itself.
  3. Cows, meet ranchers. Have fun boys. Yes, Mr. Nugent, it’s shoot to kill.
  4. Cede 99.99% of our land to Canada. Now our borders are very small, easy to evacuate.

Seriously, rabid cows? Oh now, that cow is pissed at me - I’d better briskly walk away so it can’t catch me. Briskly, I say! Lamest threat ever…

Mooooooo(ve) along.

There is the physical capacity that every person in the US can get into a car, that’s it.
Driving 1200 miles (1900 km) in 24 is not something most people can do. Moreso if you’re driving a full car.
Your example (almost) only applies if there is “normal traffic”

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As to the OP, i think we should think of ideal conditions, i.e., no need for refuelling, no toll booths, no closed roads; aside from not worrying about what happens after you arrive.