Long-period records from the National Hurricane Center show that the month of June averages about one named storm every two years. This number has remained remarkably consistent throughout the reconnaissance era (starting in 1944) and the satellite era (starting in 1966).
The graphic below shows the formation points of 84 tropical (and subtropical) storms that have formed in the month of June since 1851 and includes the two June tropical storms from 2012.
Preferred regions this early in the season include the western Caribbean and Gulf of Mexico, plus a few just off the southeast coast of the U.S.
Satellite imagery currently shows an area of disorganized showers and thunderstorms extending from the northwestern Caribbean into the southeastern Gulf of Mexico including portions of western Cuba, the Florida Keys and the southern Florida peninsula. Some computer models suggest slow development of this system as it moves generally northeastward over the next few days. Portions of the Florida peninsula and Keys should expect periods of heavy rain for the next few days regardless of whether this system develops.