There are plenty of Christian books on politics, but many of them – maybe even most of them – fail to offer much insight. Often enough they are either unbiblical or participants in the political status quo. Here are some great resources I have found.
First, there are a few classics. The “Epistle to Diognetus” is an anonymous, late second century apologetic response that offers the memorable and paradigmatic line about Christian presence and the state: “Every foreign land is to them as their native country, and every land of their birth as a land of strangers.” Then, of course, there is the seminal work of Augustine of Hippo, The City of God – the theological foundation for virtually all of Western political theology.
Second, with regard to theology, it has to be admitted that the twentieth and twenty-first century were offered few insightful contributions. As Oliver O’Donovan describes much recent political theology:
After showing how theologians of the past had been the stooges of the political forces that made use of them, political theology set out to reorder our theological concepts to the service of a suitably liberal political world-view. The proper political orientations were taken to be well understood, the shape of our theological beliefs indefinitely negotiable. 
However, there are some interesting contributions. O’Donovan has offered a dense biblical theological account in The Desire of the Nations, followed by his equally dense theological reflection on political theory in The Ways of Judgment. One can also find some of his basic ideas in the article “Government as Judgment.” For penetrating reflection on the idolatrous potential of the state, William T. Cavanaugh offered a compelling critique in Migrations of the Holy – though Protestants (like myself) will have to pardon some of his Roman Catholic convictions.
Third, there are some helpful books on the religious reasoning in the public square. Robert Audi and Nicholas Wolterstorff have given an excellent back-and-forth on these prospects in Religion in the Public Square. The middle section of James Davison Hunter’s To Change the World also reflects on the political strategies of Christians over the past few decades. Additionally, David T. Koyzis has offered an instructive engagement with various political ideologies in Political Visions & Illusions.
Fourth, there are several books that look at the practical ramifications of politicizing the church. Charles D. Drew makes a poignant appeal for de-politicizing it in Body Broken. For a sharper, external critique, Carl R. Trueman’s Republocrat offers the perspective of a native Englishman. Also, for a purely sociological look at the problem, see Robert D. Putnam and David E. Campbell’s massive work American Grace; or, for cultural history, see Ross Douthat’s Bad Religion.
Finally, it may be worth noting that American political history is far from a being the story about a new Israel – though that narrative has captured imaginations since the beginning of the United States. Mark A. Noll, Nathan O. Hatch, and George M. Marsden deconstructed it a while ago in The Search for Christian America.
In conclusion, it is worth noting a few salient details. Rightly speaking, God reigns as ruler over all the nations – he is the King over all. Nonetheless he has ordained government as a secondary institution to enact justice until the consummation of his new creation (cf. Rom 13). Therefore, our prayers and even our involvement in government are not optional! We have a peculiar perspective that keeps us from being given over to complete cynicism, on the one hand, and idolatrous obsession, on the other. So, also, the church occupies a unique place as a meta-national institution that unites even those who may stand opposed in the public realm – relativizing even while affirming that public service. Go, be actively in public life! At the same time, recognize the non-partisanship of the church – she is governed by Christ!
 http://www.ccel.org/ccel/schaff/anf01.iii.ii.v.html (accessed Oct. 17, 2012).
 Oliver O’Donovan, The Ways of Judgment (Grand Rapids: Eerdmans, 2005), x.