Unless certain Americans are carrying around very old devices, there is a special chip in their phones that ensure official POTUS messages can always get through, no matter what. Phone manufacturers are required to include these chips in US devices, due to an extension of the country's Emergency Alert Network enacted in 2012 that allows the president to get in contact with anyone, anywhere, whenever necessary.
The chip allows phones to receive presidential emergency alerts when they enter a specific geographic area. Technically, it's not actually a text. (So you'll never see Sent From my BlackBerry on Obama's emergency warnings.) It's a specialised message form developed for emergencies.
These warnings have a unique vibration and sound alert, and they're sent to any phone within a geographic radius of a cell tower. Unlike Amber Alerts and weather emergency alerts, there is no way for Americans to opt out the presidential text service. It's compulsory.
Image by Whitehouse/Pete Souza