Forgot about LBJ but I think Nixon was a Congressman.
He was a congressman from 1946 to 1950. He ran for Senate in 1952 in what was probably going to be a losing bid, only to have the incumbent drop out midway through the race. He won the Senate race by a huge margin, which is what made Ike want to pick him (on top of the Hiss stuff).
See his official biography here: http://www.whitehouse.gov/history/presidents/rn37.html
It mentions briefly.
It's not well known, since he served only 2 years in the Senate before being picked as VP, but he was indeed a Senator. I learned about it from reading one of his books.
Oops, I meant he ran for Senate in 1950 and was the VP pick in 1952.
So yah, Congress 4 years, Senate 2 years, then VP.