Yes, they do. But... Members of Congress get their security clearances merely on the baseis of a promise not to reveal secrets...unlike others, who have background checks, interviews, etc.
I’m pretty sure that if a Senator or Rep. was on a National Security committee, i.e. Armed Services or Homeland Security, then that person would have to be checked thoroughly. This morning I heard a man who does security checks for the CIA and FBI say that Obama certainly could not get a security clearance, based on his past aquaintances.