It's a toss up between Janeway and Picard for me.
Picard is an easy favorite, because I feel like he would have no fucking time for political games in D.C. He'd likely be very good at tuning it all out, and also as perhaps the most egalitarian of all the Captains, he wouldn't give two fucks about what some donors or corporate lobbyists want. He'd put country over party as well, which I think would be a nice refreshment.
Janeway on the other hand would seem like the most willing to reach out and work with her ideological opponents to get things done in a pragmatic fashion. Which is kind of a double edged sword, but does hold some value. She is also one of the more willing Captains to admit when she made a mistake, something I think Picard would be a bit uncomfortable doing.