Not Long
From Key West there are choices of how to get West depending on the wind direction. If the wind is heavy from the South you can go up the NW channel and past Smith shoals and get there from the Gulf of Mexico. I usually like to go outside in the Florida straights so I can fish in deeper water but the swells are larger and after a couple of nights on Duval Street sea sickness can set in. It is about 70 NM to the Tortugas but the Marquesas keys are about 3/4 the way there and a good stopping point. You really are not out of site of land for very long. Coast gaurd, Customs, ATF and others patrol these waters and a helicopter is just a few minutes away.You need to be totally self suficient as there are no supplies of any kind sold or given in the park. no trash bins either, all trash goes back with you. Your only real difficulty would be the weather,June has big thunderstorms which isn't a real big deal as they move thru quickly, I would be more concerned about Tropical depresions. The water in the Tortugas is a georguous teal blue and is teaming with marine life. Diving, snorkleing fishing swimming and dinner on the BBQ under the stars, life is good, enjoy I am envious!