The emergency alert system has been used here in Minnesota for tornadoes, amber alerts, and flash flooding. Sitting in a room and hearing every phone go off or waking up to your own phone making the warning tone is quite alarming.

If I received one about a nuclear missile I'd assume it's legitimate and at least take some minor precautions while trying to verify the alert. It's foolish to assume every unlikely alert is a false alarm.

That said, a single nuclear missile seems incredibly unlikely to me. I'd expect multiple missiles and an associated cyber attack if another nation state was willing to start a nuclear exchange. A single missile is just inviting the wrath of the US and rest of the world for little benefit.