I was always of the understanding once you were deported, you could not longer enter the U.S. So I think legally if you are deported, you are supposed to be out for good, and if that is the law, that is the way it should be. However, altho’ I adore Ted Cruz, and his “rule of law”, he needs to get a ruling on his citizenship issues before he takes us all down the yellow brick road.
I believe being here illegally is a misdomeaner for a first offense and a felony for a second/third/etc offense. Felons are most likely barred from immigrating. So I’d think one deportation does not in and of itself disqualify someone from immigrating.