It's also what the President seems to be advocating we allow them to do. Or at least excusing them if they get caught. Above and beyond even that is the Presidents proposal to fork over our tax money to them. That money should see to our own national needs BEFORE it is ever considered for use elsewhere. Without a few billion going to Africa, a few more billion going to South America, and only the Gods know what else in foreign aid giveaways... we could probably get the budget way back under $2 trillion again. Easily.
$68 BILLION was lost because of illegals sucking up resources. Their taxes from picking turnips isn't gonna put a dent in that. Especially once they start drawing even more benefits legally. This'll make the Presidents Viagra give-away look frugal by comparison.
Illegal immigration has got to be stopped but at the same time we have to keep legal immigration quotas in place. No way could I support open-ended immigration, even if it's legal.
Everything else you say is correct, stop the foreign giveaways and end the welfare.