The vast majority of immigrants from Latin America come here to work. If not for the employers who are looking to skate around labor laws, they would not be here getting those “entitlements” you so abhor.
Quite frankly, if the employers were forced to use E-Verify, it would significantly cut the flow of illegal immigrants across the border.
And I would like to place the blame exactly where it belongs: on the employers. Even if we allowed immigrants to freely cross the border, but required their employers to pay for all of the “entitlements” given to these employees and all of their dependents, then I think most Americans wouldn’t be nearly as bothered by illegal immigration. Also important would be to ensure that all incoming immigrants are not criminals, and if they participate in any illegal activity while in the U.S. (including tagging/graffiti, petty theft, etc.), that we deport them immediately and ban them from ever entering the U.S. again.
Ultimately, we are subsidizing the employers with those entitlements because they don’t have to pay a living wage and nor deal with those pesky labor laws when they use illegal labor.