Fame is short-lived. Fame can be fickle. Fame can be a dubious goal for a senator. If you want to hold public office because you want to be famous, you probably should move on to the next table at your career fair. Fame is for celebrities.
Senators don't need to be famous. Just ask Frank Lautenberg, D-New Jersey. Never heard of him? He was born in 1924 and at 88, he's the oldest member of the 112th Congress. He was first elected senator in 1982.
By design, Senators are supposed to represent diverse populations and interests and so should be flexible and their interests transparent. Being famous for being cooperative and scandal-free could put you smack dab in the middle of the road, a weirdly safe place to be.
Don't forget, politics is about popularity. You may have a law degree from Stanford and a genius IQ, and you may have launched a Fortune 50 company…elections can be a lot like Project Runway: One day you're in, and the next you're out.