For Evangelicals*, the seminal work on this very question is Kingdoms In Conflict by Chuck Colson. (Note, the book has been since released for those unable to handle anything less than a summary in its title, as God and Government: An Insider's View on the Boundaries between Faith and Politics.)
Chuck Colson - special assistant to President Nixon during the Watergate coverup turned Christian after his involvement became public - had a unique perspective, in that he was a high ranking government official who became a committed Christian.
In a nutshell, the thesis of his book is that Government was ordained by God for one thing - namely to keep order, and the Church for another - to point souls to God. The conflict between these two stems from those times that the two purport to invade the other's sphere of responsibility.
That citizens are afforded the right to vote, however, informs Colson that individuals are vested in each sphere too. Although we are "aliens and strangers" (Hebrews 11) in this world, we are also called to "pitch our tent here" and be the incarnation. We show love to our neighbors by participating in the process.
Ulitmately, where each individual draws that line - between being "in the world" but not "of it" - is one that is not clear in Scripture. David was wholly political, but also a man after God's own heart. William Wilberforce and Martin Luther King, Jr. were political precisely because they were Christian. Conversely, Baptists would also lift up Roger Williams, the founder of Rhode Island, who started his own colony precisely because he felt the Puritan Reformers of Massachusetts had so thoroughly negated this line.
That we have been afforded the right, as citizens, to influence government in this time and place is a privilege that many would see as a gift of God. To spurn that offer seems rather ungrateful to many.
Note: What separates Evangelicals from Fundamentalists is precisely this point. After the 1925 Scopes Monkey Trial, most Fundamentalists retreated from the culture as a whole, eschew political involvement. Evangelicals like Billy Graham and Carl Henry were muchly responsible for pulling a segment of that tradition back into the place where they would engage the culture, forming the basis of the modern evangelical movement.