Christian Republicans

I've been thinking a lot lately about the major contradiction in beliefs between Christians and Republican'ts. Let's examine:

Christians:
-Help the poor, sick, and "least among us"
-Never judge thy neighbor
-Give away your possessions so that the less fortunate may have comfort
-Be kind in spirit
I'm pretty sure these are the things Jesus preached, albeit in a more condensed format.

Republican'ts:
-What's mine is mine, and you don't get any
-Welfare is for lazy people
-Avoid taxes at all costs, even though it means poor people may go hungry
-Privatize healthcare so that only the rich can get medicine
Again, this isn't meant to characterize the entire GOP platform, but I'm generalizing here.

I really can't wrap my head around why these two groups are so intertwined.  Christians today seem to ignore the "help your neighbor" part and instead focus all of their energy on abortion and gay marriage, neither of which Jesus actually spoke about.

Ive heard some of these people tell me that it's the church's job to care for the poor, not the government's, but if the government has a much more effective way to care for the poor, say, through Medicare or food stamps, shouldn't they support that?  I mean, you can't guarantee that all people live in a place with a particularly helpful church, but you can insure that everyone in America gets help with Federal programs and public education.

Where is the connection that I'm not seeing here?