Giving them permission to stay and work or study, provided that they buy and renew permits and obey the strictures of the program, doesn't seem like such a stretch, nor does it amount to amnesty, particularly considering this is a group of people who were brought to the US as minors.
As for overreach, such "deferred action" programs have been ruled constitutional. There are certain elements of DACA that are on shakier ground, but calling the whole thing "overreach" is overstating the case.
Simply as a practical matter, how is our country improved by rescinding the legal protections assigned to these people?