They spooled up pretty quick for the Haiti earthquake, I believe it was a matter of four or five days.
Those ships are an awesome resource.
I remember reading, but can't find the source, that in the case of the USNS Comfort, the plan is to take it to NYC and divert trauma cases to it. Clearly they'll have to assume anyone they bring on board is infected, but their primary job will be to intake all the New Yorkers who wind up getting in car crashes, get shot, get stabbed, fall of buildings etc, and take some pressure off the other hospitals.
Not sure what the plan is for USNS Mercy. San Francisco would be high on my list of possible destinations though.
Edited because I had the names of the ships swapped.