Jesus would agree with welfare and socialism. Helping people is of huge emphasis in the synoptic gospels, arguably the only 3 books of the New Testament that Jesus would have had a hand in. The "conservatives" in America today are nothing but hypocrites who want the government out of corrupt big business and lobbying, but only if it helps their causes. If it has anything to do with environmentalism, abortion, marriage equality or anything "unchristian" like that, they hate it and call it liberal propaganda. They do nothing to help the poor or downtrodden.
I believe he'd agree with socialism, but on a small community scale that has God as its roots and not government. I think History has proven that communist and socialist governments are self-defeating. Why? Because man, without religion, is not looking to work extra hard only to help his fellow man. Eventually that spirit in the society fades, and capitalism must again take hold. That's why China is largely capitalistic now even though it was once extremely communistic. Communist communities based on religion can work; communist governments are naive. The church has repeatedly helped the downtrodden, and I don't think we need big government for that. Big government spells big bureaucracy. It's as has been said before, "The only thing that saves us from the bureaucracy is its inefficiency." Big government spells corruption - not efficiency.