Bills have been proposed in the past, and when the Americans got wind as to what was going to be passed, called their Representatives and demanded otherwise, AND the bills died. Unfettered access to America will not fly.

A clean bill which would allow the Dreamers to stay is called amnesty. A bill which would allow them to stay with the provision that the border get secured has a much better chance to pass. 

Also, let them stay with NO chance to participate in the electoral process.