After giving it some thought, I'd say this falls into the category of Matthew 18:15-17.
15 “If your brother sins against you, go and tell him his fault, between you and him alone. If he listens to you, you have gained your brother. 16 But if he does not listen, take one or two others along with you, that every charge may be established by the evidence of two or three witnesses. 17 If he refuses to listen to them, tell it to the church. And if he refuses to listen even to the church, let him be to you as a Gentile and a tax collector.
I'm hopeful that his closest brothers followed this. That they went to him first alone, and then with one or two others, and then with his church. And I consistently hope that those things work, because when it comes to verse 17, I don't much LIKE verse 17. I don't want anyone to be cast out, or turned away, or treated as a proverbial tax collector. Of course, it isn't up to me. (And I'm grateful for that, because to be honest, more times I act like the disciples in Luke 9:54...)
In terms of handling the "Christian as a man, but not as a politician" or "representing your constituency" I think there is a beautiful and perfect solution for this: Act like a Christian in private and in public. Don't be two people, be one. Be the one you're supposed to be. Run on the platform of your values. If you don't get elected, that's not really your call, yeah? Your call is YOU. We are consistently called to personal responsibility, time and again. Sure, help the world, but always start with making sure YOU are doing what's right. And if you DO get elected, great. You never have to lie to your constituents. You ran on "I will act this way" and you act that way! And that may seem idealistic or even naive, but frankly I think "that's naive" is often used as an excuse not to do it. Shouldn't we, as Christians, be idealistic? We can be in the world, and understand how it works, but the moment we become of the world it all starts to fall to pieces.
My thoughts, anyway. If someone were to disagree, I doubt I'd fault them. If I myself disagreed years from now, looking back, it wouldn't surprise me. But that's where I'm at right now.