The Christian model of dealing with government is fundamentally incompatible with living in a democratic country, anyway. It teaches to always submit to the government's authority unless they actively tell you to stop practicing your faith, in which case you turn yourself in and let them nail you to a cross. But in a world where governments are not only no longer allowed to do that to religious people but the masses have a civic duty to participate in the democratic process, the moral imperative to submit to authority becomes a paradox. If you vote for those who favor your values, you're bossing around the people who ought to be bossing you around. But if you purposely refrain from voting or actively vote against your own interests, you're failing in your civic duty which is a form of rebellion in its own way.
(You'll notice, by the way, that everywhere else that Christians are instructed on how to deal with those who have power over them, said power is always framed as absolute—for example, Paul speaks on how slaves should behave towards their owners, but never on how free workers should behave towards their bosses. Presumably, in Paul's version of a perfect world, such vague relationships would not even exist.)
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