Article from the Washington Post here.
There is little urging on the part of Paul to give up your possessions to government to provide for others. There is an urging, by both Paul and Christ, to be ambivalent toward things like taxes. Pay them, because your rewards are in heaven, not because they are a good thing. Your earthly possessions, just like the earthly rulers, should be irrelevent to you, as your rewards, just like your true ruler, are in heaven: "Give to Caesar what is Caesar's, give to God what is God's"
Read the gospels and you'll find that Jesus was extremely opposed to any interaction between belief and political power. Not that He is particularly "anti-government" per se, but He is ambivalent. What matters is the kingdom of heaven, not the kingdom of men. When the two become united you have a group like the Pharisees who turn earthly laws into metaphysical salvation.
Earthly political rulers are however, viewed negatively (Pilate, Herod, the Pharisees). Tax collectors are also viewed as scum (i.e. the pharisees criticizing Christ for friending "sinners and tax collectors"; Matthew the tax collector; Zachias the tax collector; etc.) The fact that the author seems to overlook the constant discussion of taxes and tax collectors throughout the gospels is indicative that he is either being hostile to the senator from Oklahoma for little reason, or he simply is arguing about the content of the gospels without actually having read them.
The author is claiming that the Deuteronomical demands on provision to the poor are somehow justifications for taxation by government. The Exodus and Deuteronomy passages are requirements for living in the religious community, demands saying that as part of your belief, you must also contribute to the poor, similar to the demands by Peter in the book of Acts. Providing for the less fortunate is a function of the fruits of the spirit, not secular governance.
The long and short of it is that libertarianism is not contradictory to Christianity (as Miss Rand would have us believe), nor is Christianity contradictory toward libertarianism (as liberation theology would have us believe). They are not however clear justifications for one another. One is a view of the kingdom of men, and the other is the kingdom of God. What they do have in common is individualism. Salvation is through faith between an individual and God, no earthly ruler may intervene. Indeed, libertarianism as an extension of classical liberalism, is born of the reformation movement of "sola scriptura", refocusing Christianity on the text of the gospels (not traditions of the catholic church). Part of the text of the gospels is the foundation of individualism (Salvation by Grace through Faith).
Senator Coburn is right however, and the author of this article apparently is lacking on both theology and political science. The compassionate conservatism of George W. Bush and Mike Huckabee is not Christian. There is no justification for government redistributing wealth in the gospels.
While unrelated to the politics of the gospels, the author's assertion that private charity and the free market cannot combat AIDS or replace medicare is complete nonsense. Most charity regarding the AIDS virus in Africa is done through private funding. The proportion of elderly and poor people recieving care prior to medicare and medicaid is the same as it is today. Private charity did just as good a job taking care of the poor and elderly, while simultaneously keeping costs low for everyone else. Imagine that.
The main problem with deriving earthly political systems from Scripture is that the future kingdom of God (the new Jerusalem, "The LORD Is There" - Ezekiel 48:35) is based on an infinite supply of free resources provided by the infinite grace and power of the Almighty.
There will be no more hunger because God provides directly for his people, per Revelations, and the curse of working the land is gone: every need will be met without effort, meaning all economics cease to matter (with nothing valuable to trade).
However, for this present world, the New Testament stays silent on the issue of government, except (as Patrick points out) to say "pay your taxes" and "do not rebel against those set above".
The Christian response should always be to feed the hungry and clothe the naked, treating the least of society as though they were Christ Himself. That is the individual responsibility of every believer.
This is vital: we have to feed and clothe the poor. There is no evidence to suggest that we may use governmental theft of other's property to help relieve ourselves of this responsibility.
Murray Rothbard, while not a Christian, describes the situation of Paradise in the first chapter of Man, Economy, and State. While obviously it's his perception, he describes it as a state in which economic activity does not occur as ends are acquired without employing means. He describes this to illustrate the reality of human action in the temporal world, but I think the juxtaposition of paradise is a good one.