That is hardly true. Making their lives here impossible would do the trick. They cannot start make their own job if they cannot get insurance, drive, rent or buy property, get an ID card, send their kids to school, have a bank account, etc. Like you said, if their lives are miserable, they will pack up the family and find someplace better to live. No need to go door to door if they leave on their own.
You really have no clue about immigrants, do you? They will find a way around every single hardship you just listed -
I know this because I've seen it myself. Not only that, but thanks to the laws of supply and demand - you know, that free-market altar before which all conservatives kneel and pray - when there is a need for illegal immigrants to do any of those, there will be those who can fill that need, one way or another.
Wanna drive them all out? Sure, you can do that if we send armed people from door to door in every town and city and metropolis, demanding "papers please" as brownshirts did in a certain nation about 70-odd years ago...but is that the kind of America you want? Is it really? Maybe it is, if you're the type who likes to cruise on over there to the Stormfront site.
So you've got a choice - you can either stick by America's tradition of being an immigrant nation from our very founding...or you can go the route of nativism...which we have seen too many times before tends not to end well.
It might also do you well to remember a certain poem on the Statue of Liberty, "The New Colossus":
Not like the brazen giant of Greek fame,
With conquering limbs astride from land to land;
Here at our sea-washed, sunset gates shall stand
A mighty woman with a torch, whose flame
Is the imprisoned lightning, and her name
Mother of Exiles. From her beacon-hand
Glows world-wide welcome; her mild eyes command
The air-bridged harbor that twin cities frame.
"Keep ancient lands, your storied pomp!" cries she
With silent lips.
"Give me your tired, your poor,
Your huddled masses yearning to breathe free,
The wretched refuse of your teeming shore.
Send these, the homeless, tempest-tost to me,
I lift my lamp beside the golden door!"
That, sir, is what has made America great - the renewing drive and determination of immigrants who keep our nation from stagnating. That, sir, is America. Love it or leave it.