As for the poll questions:
Deportation of illegal immigrants?
About right. The current policy works fine and I already pointed out that the Obama government deports people like no administration before.
Should illegals with American-born children be exempt from deportation?
Yes, there needs to be a social component here, because what should a 7-year old kid in the US who goes to school do with deported parents in Mexico ?
Should there be an automatic birthright citizenship for children born to illegal immigrant mothers?
No, automatic birthright citizenship shouldn't be possible.
Should a person have to prove they are in the country legally before recieving government services?
Yes of course. In Austria, foreigners even have to work a few years and pay into the system before they can claim any government services.
On that last thought; illegal immigrants do pay into the system; they pay sales tax, most kinds of payroll tax, and other taxes that don't specifically require legal residency.