The the notion of private property is firmly ensconced in the Bible: not just personal property but real property as well. Socialism, in its severest form, does not allow for private property and has a limited view of such in its more pragmatic forms. If God's design for the society of his people as espoused in the Old Testament gives us any clue, means of production are intended by God to be held by individuals as a basis of self-reliance and freedom for those individuals and their children after them. Political authority exercised over the individual's talents and the individual's use of his property was considered by God a detriment, not a noble goal.
Furthermore, trying to obliterate class distinctions in society is a fool's errand. Jesus said the poor will always be with us. In the kingdom, even in the eternal age, there will be distinctions in rewards. The petty jealousy of the natural human heart which can't stand seeing someone else have something that it does not should not be the driver of public policy. However, the economically powerful should not be allowed to benefit themselves while squeezing those that make their wealth accumulation possible. An equitable share of profits going to workers is good policy, whereas equality in earnings is a hopelessly misguided fantasy.
Personal initiative and responsibility is the foundation of personal righteousness. Taking care of the helpless, the resourceless, and the weak (the poor, widows, and orphans) is a biblical construct, but transferring personal responsibility to society is not. Whereas "helping the working man" fits within a biblical framework, welfare for the able but idle does not. In taking that concept to the nth degree, we hear the convoluted logic today that considers universal healthcare (or really, anything else that must be earned by the able) an inalienable right.
People, all of them, are sinful by nature: if there is a way to get without giving in return a sizable proportion of them will opt for that choice--some more, some less. This is just the reality of human nature. To assume that big government is capable of equitably administering the crash between demand and supply which will result from a policy of open access for all seems to me the most hubristic conception to come down the pike in the modern age. Supply will become inadequate and prices will rise despite the best intentioned interventions of socialistic public policy.
Sometimes socialism is said to be a biblical idea due to the experiment of the early church in Jerusalem. I would note that the model was not repeated anywhere else the church was planted; that Jerusalem was a pilgrim city where many would have been in town on a temporary basis without visible means of longer term support; and that the area was poor and subject to drought and shortage. People liquidating personal property to help out brothers and sisters in distress was never meant to model communal living, the weight of NT scripture makes that more than clear. So much, then, for "biblical socialism."
Concentrated human authority (e.g., a king) is not God's desired option for the government of his people. By extension, any authority (king or not) that can confiscate property, conscript sons and daughters, tax parasitically--in other words, endanger personal freedom--is not what's best for God's sons and daughters. Human beings are sinful: put power in their hands over others and they'll use it sinfully. Socialism, even if democratic, ignores this reality and puts sinners in stifling control over other humans.
Can such a thing ever be expected to produce anything other than bondage?
Should Christian voters support overreaching governmental control in America, or curse our descendants with the burden of a relatively large, permanently underemployed, feckless welfare class akin to what exists throughout socialist Europe? American believers are free to join unbelievers in constructing a Tower of Babel against acts of God (that is what socialism seems to be an attempt at to me), but it won't be the Bible that influences such a choice. The Bible, as I see it, is relatively clear in its support for personal property, personal responsibility, economic freedom and trusting in God. Socialism, on the other hand, can only produce the tyranny of the sinner.