Very long...possibly as long as 3-6 months in some cases. Though the benefits are better and the work is typically easier, it's still a bureaucratic nightmare. I would look at other jobs in the meantime. You may want to take a PRN or float pool job and scale back your hours once you are fully hired.
I interviewed for an RN position on an army post and was told that the fastest the hiring process could possibly go once the official offer was made would be three months, and that it might take as long as eight if the background check was complicated or the person in charge of my background check was slow/new/overloaded/whatever.