A travel calculator shows that it takes about 22 hours to drive from Florida to Canada. Given detours and stuff that might have to be made in the face of the apocalypse, I can double that to 44. If the group was to drive 8 hours a day, and they could probably do more, it would take 5 and a half days of driving, i.e. way less than the two weeks we have to do ingame.
I had the same thought. I read the book Paper Towns, and in it the characters make it from Florida to New York in a minivan in less than 24 hours without stopping to sleep. They even showed all the numbers and calcuations for traffic and such. Even the Short Road Mode is a bit of a stretch.