Although quite a number of citizens feel like that, I don't think the great majority are going to insist on it if the bill also guarantees a shut down of the border. I believe the majority will concede the former to get the latter.
It's just not possible to "shut the border down". Americans aren't that naive to believe that allowing 15 million people to go to the head of the line in exchange for a promise on a piece of paper will stop the illegal alien flow into America....and it's a slap in the face of all legal immigrants who came here through the current lottery system. Reagan's amnesty failed. The only way is to have the illegal aliens leave and take their proper place at the back of the line.
No one in authority said to the "front of the line." Red herring, period.
If they are placed at the back of the line after being vetted, then that is not a slap at the legal immigrants.
No one is going to round 11 to 13 million illegals. Americans as a whole will not permit a police state atmosphere that threatens the citizens. Just not going to happen.