Remove illegal immigrants ability to receive benefits from US welfare.

I would like to make it impossible for non-US citizens to receive benefits from our welfare systems in the US. If an illegal immigrant were not able to receive benefits such as; food stamps, WIC, housing, unemployment, etc, I believe it would be a step in the right direction for shrinking the immigration problem we face today, as well as assisting in getting poverty stricken Americans the help they desperately need by freeing up misapplied money. How can we say these welfare programs are failing, when it's we the people allowing to fail by allowing non-US citizens to feed off US taxpayer's money while not paying taxes themselves.