There are two main groupings on the Right. First, those who feel that the less fortunate are lazy, get what they deserve, etc. These are the folks who have, more than any others, given conservatives a bad image -- the Left tends to see the entire Right as having this attitude.
But there are also those who may be committed to aiding others but believe the government should not be involved (or be as limited as possible). There are many good people who feel this way and they do have some valid points. It's never a good idea to give too much power to the government nor to let it co-opt working independent solutions.
I have always felt that there needs to be a balance between the two, the governmental and the private. Neither can nor should do it all in our current society.
We should keep in mind that when Jesus told us to feed and clothe the poor and the hungry he meant US, not the government. He didn't tell the Roman authorities to do it.
Now there is nothing wrong with us working through the government to accomplish this, in part. Moreover, it is certainly necessary if we wish to establish a stable society. Government needs to be involved for its own good -- having people starving on the streets would destabilize any nation.
So the government needs to provide a basic 'safety net' for its citizens. How big that net need be is open to debate.
But the answer, of course, is 'just big enough.' :)