As of 11pm EDT June 13th, it has been 1003 days, 19 hours, and 50 minutes since the last landfalling hurricane in the United States. That was Hurricane Ike that hit Galveston, Texas on September 13th 2008 at 3:10am EDT.
That's the longest stretch of time without a landfalling hurricane in the U.S. since 2002 when hurricane Lili made landfall in Louisiana on October 2nd, which was 1083 days after hurricane Irene made landfall in Florida in October of 1999.
(Hurricane Ike making landfall in Galveston on Sept. 13th, 2008)
The Tropical Atlantic is quite right now and is expected to remain so for the next 5-7 days. One of the reasons is a Climate Phase called the Madden Julian Oscillation, named after the scientists that discovered it. When it is in a positive phase like it is now, it favors sinking air and higher surface pressures in the Atlantic. It is forecast to switch to a negative phase in about 7-10 days from now. Then rising air and lower surface pressures will exist, which is a more favorable environment for tropical cyclone development.
At the end of June last year there was favorable conditions in the Atlantic and an African Easterly Wave wondered into that environment and we got Hurricane Alex, a rare June hurricane. There is strong wave coming off of Africa right now that will be entering the Caribbean at about just the right time. Some of the long range forecast models are already picking up on this as a possible tropical storm in about 10 to 14 days.