Illegal immigrants do not receive welfare, unless they have a child born on US soil (and are deemed eligible for US citizenship), in which they only receive the benefits granted related to that child.
People who say "Open our borders" want immigrants to cross in a legal manner, where they are documented and accounted for. Nobody wants people climbing fences and making a run for it. Thus, the analogy should be "knock on their door and ask if you can come over for lunch", in which case that's just being a nice neighbour.
I'd be willing to bet that the average American taxpayer pays more tax money per year towards corporate welfare than towards welfare for those in poverty. Welfare isn't the reason you're poor.
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http://www.youtube.com/watch?v=XiCtAUrZbUk -- Defeating the Running Man of Ocarina of Time in a race since 01/17/2009. --