I've never done it, but it wouldn't hurt to contact your house representative and senator and ask if they have tickets for the Kennedy Space Center you could get. Many people have reported that congressional staff used to at least get some free tickets that they typically give out each year and that they had success getting these just by asking. Maybe it's "Ask and you will receive."
It was pretty easy when we went to Washington D.C. to get White House and Library of Congress tickets, I know.