People would be able to travel in the streets to be evacuated. You can survive heavy radiation doses for a short time. I remember talking to a friend who photographed inside a nuclear reactor after an accident in the fifties. He said the film was so badly fogged by radiation that they had to go back in and re-shoot it.
A ground burst would not cause nearly the fire damage that an air burst would because the most of the city would be shadowed by the nearest buildings.
Lack of water, electricity and refrigeration are pretty much standard inconveniences that we deal with during disasters.
Getting that many people out of the death zone is not a matter of a "short time."
We may need to rethink a LOT of policies--such as the desire to stuff as many people as humanly possible into close quarters and call the result "urban planning."
A ground burst would not cause nearly the fire damage that an air burst would because the most of the city would be shadowed by the nearest buildings.
But the fires that DO start will not get put out, and will continue dumping secondary activation products downwind, complicating evacuation efforts (and, incidentally, dumping those products in now windowless buildings that you're using as fallout shelters.
The evacuation process itself would kick up an immense amount of radioactive crap for everyone to breathe in.