I'm probably just echoing at lot of what has already been stated, but hopefully this is additive rather than just parroting.
As a Christian, I do believe in a communal responsibility to my neighbor. After all, I am to love my neighbor (even my enemy), which means I am to help care for the poor, the sick, and the unfortunate; but it als also means, I should support the rich, the healthy, and the fortunate--just in different ways. This is a personal responsibility I have and it is why I give up a lot of my time as a teacher--where my G-d given talents rest--to my community. It is also why I give financially whenever I can, but keeping in mind that I should avoid, when possible, giving to the point where I become a burden on anyone else.
This financial support starts with my own immediate family, so they are not a burden on the extended family. I then support my extended family, so they are not a burden to the community. Then, I support my community (for me that is my congregation), so they are not a burden to the society. Finally, I support the society. This working from the closest and most direct, to the farthest and most removed is the form of charity I believe the Bible teaches. By behaving this way, it requires me to actually show love toward my neighbor, for often this type of support is more demanding of me that just giving a few or a lot of dollars to a charitable organization. For example, take giving $$ for Katrina or Haiti relief. While it makes me feel good to give money, at least temporarily, I am often left with a sense of how little I actually gave of myself and how I failed to show love. A real expression of love would be to go to Haiti to physically help the people or adopt a Haitan orphan.
Now all of that is addressing how I believe I as a Christian should act. When you bring the government into the equation, it becomes a lot more complicated. First, I am commanded to obey the government and to render onto Caesar what is Caesar's. Therefore, if the government requires money or other things of me, I am to give it as long as it does not cause me to sin--i.e. violate G-d's commandments. Thus, if government taxes me to support my neighbors, then I pay the tax, even though I do not see that as an act of showing love to my neighbor--after all, the tax is coerced, not given by a willing heart. And when I think of how I could have used that money to support the needy in my family and community, where I would have given out of love, it does bother me. Nonetheless, I give it to the government.
In addition to all of this, there are also my political views, which result in having little faith in governmental institutions, especially those most removed from the individual--i.e. I have a lot of faith in local government, essentially zero in the federal. Thus, even though I give to Caesar what is due, I don't expect Caesar to use that money wisely, efficiently, or morally. Add to this distrust, the fact that I am a Tocquevillian conservative, by which I believe the more an individual gives over to government to take care of the community's needs, the more the individual diminishes himself by becoming less concerned with those in his community and the more tyrannical the government becomes because the individual selfishly relenquishes his power and authority to the government inorder to take care of his neighbors, so as not to be bothered by them. Finally, I view federal and state government institutions to be in competition with the family and the local community for loyalty and resources. Therefore, an increase in government power, finances, and regulation means a diminishment of family and communal power, finances, and regulations. (All of this is a messy and unorganized expression of my political beliefs, but there isn't time to expound upon them).
Anyway, that is my abbreviated answer to the question of the thread.