No. Jail is WAY too expensive. Why should we waste on money on these vagrants?
How about this:
1) Enact a stronger version of CA.'s prop 187 nationwide. No welfare/food stamps/head start/WIC/Housing, health benefits, and most importantly, no public school for their kids.
2) No work withjout proof of citizenship or a valid work visa. And we should eliminate work visas until there is 0% unemployment among native born Americans.
3) End birthright citizenship.
Do these things and they will be trampling themselves to scramble back across the border.