I don’t think this headline means what its author tried to convey. When I first read it, it seemed to say that signing up for Obamacare will save relatives from deportation. But, when you read it, the President said that signing up for Obamacare will not attract attention from the government that will lead to deportation of relatives. There is some kind of misplaced modifier. “Because” is certainly not the right word. Maybe “if” would work better.