The rationale works like this - given that some less-fortunate members of society will need assistance at some point in their life, and given that 'conservative' != 'asshole' and we don't want to just let them die in the street, we have to provide some form of limited welfare state.
Since we have to provide some form of limited welfare state, what's the best way to do it while preserving as much freedom as possible? We could set up a large government bureaucracy to do this, with rules and regulations and intrusive measurement for determining who can get what, or we could simply periodically cut everyone a small check.
Hayek thought the small check was a lot less harmful than the large bureaucracy. I'm inclined to agree.
It'd be better still if the government could get out of the welfare business altogether and leave it to our individual communities - I certainly don't mind that my synagogue dues are used to help our poorer members, and if my tax bill was lower, I'd have still more to donate. But that would require a cultural shift to make practical - it's a shame, but most people in America no longer belong to small, supportive communities.