My answer is similar to Nemo's.
I'd give illegals 120 days to sell any property and get out of the country.
From 121 to 180 days, illegals would be given six months of hard labor (if they don't work, they don't eat) then be deported.
After 180 days, the hard labor jumps to ten years.
Citizen children of illegals could stay if they have a legal custodian, or leave with their parents and lose their citizenship, or be put up for adoption.
It would need a little tweaking but it would work.