"I think you could get support for a Constitutional Amendment to get rid of the anchor babies. "
You mean to change the Constitution so that you can't claim citizenship unless you're born here of legal parents? Oh, sure you could get support--from about 20% of the public.
I'd never support such an amendment and I don't think it will ever come to pass.
You're wrong, you'd get the same 80% to support it that support stronger enforcement. And make no mistake, amending the constitution to end the anchor babies will definately come to pass.
You are in the 20% minority that would not favor such action. Not good company for you and your desires.