I took your phrase “accomplished in getting things done in Washington” as ruling out those who only had experience as Governors. Sessions did come to my mind as a possibility. I wouldn’t touch Rubio or Christie personally, and was thinking that your simple description arguably does produce a null set.
The reason why we have none of our people in Washington is that when they get to Washington, they cease to be our people. (Reagan, perhaps slightly misquoted).
What about Marcia Blackburn? I don’t know much about her, except that she seems to be a highly regarded and effective Constitutional Conservative.