The Constitution demands equal treatment of persons within its jurisdiction, regardless of their nationality. Thus, the whole immigration regime is un-Constitutional. Letting people, who come into the country with lots of money stay as long as they like, while people, who trade their labor for pay, get expelled, is unequal treatment.
Moreover, legislating restrictions on the human rights (to migrate and associate) of people who aren't even within the U.S. jurisdiction at the time the legislation is designed to apply is doubly un-constitutional. The law, as it applies to individuals, is supposed to prohibit and punish injurious behavior -- i.e. the deprivation of someone else's rights. Migration and association and, indeed, perambulation, are all natural and good behaviors.
While it is not unusual for Congress to make laws depriving individuals of their human rights (DADT, DOMA, Immigration, Volstead Act, Military Commissions, etc), it is still wrong and it needs to be challenged in the courts. Perhaps the ACLU should file suit on behalf of the people who have already been expelled and deprived of their families. It seems strange that foreign nationals (Hamdan and Boumediene) should be the vehicles for affirming U.S. Constitutional principles, but there it is. Perhaps suit can be brought on behalf of the children. The Pontius Pilate response just won't do.