People have a tendency to worry about new things. We have lived with nukes so long that we cease to worry about them, and think about the dangers of new things. But frankly, we just got lucky during the cold war. There were a lot of very close calls that would have resulted in a nuclear exchange.
Of course, the risk of our country being wiped out by a nuclear exchange is lower than it has been at any time in the last 50 years. And Obama continues to reduce that risk:
For the first time, the United States is explicitly committing not to use nuclear weapons against nonnuclear states that are in compliance with the Nuclear Nonproliferation Treaty, even if they attacked the United States with biological or chemical weapons or launched a crippling cyberattack.
I would have preferred a stronger 'No First Strike' promise, so that Russia and China would be more confident that anything that looked like a launch was probably a something else. But anything that shows that we are committed to limiting our use of the weapons should make everybody less worried, and less likely to make a civilization-ending mistake.