WHY? How about warning whole population?
This always amazed me about US. President is not a god, he is just a function, there is a hierarchy of replacements. Why do you keep making one man above all citizens?
It is unlikely that the US can defend from an ICBM, although if warned in time, the President can survive and then command a retaliatory strike.
US President is probably the weakest world leader by far. He's extremely constrained by Congress, and can't even negotiate a treaty without Congress breathing down his back.
But in a war situation... which a nuclear strike would definitely be... the first priority is to keep the Commander-in-Chief alive so that he can organize the counter-assault. That is his job after all.
Sure, the President as Commander and Chief can be replaced, but there could be a lot of confusion and time taken in the process, especially if many of the people in the hierarchy are also killed or otherwise indisposed.
With that aside, a presidential death, homicide or otherwise, would be extremely jarring to the US population. Ask anyone who was alive when JFK got shot. And plus, if there ever is a major national crisis, we would need a strong leader with a strong mandate, not someone who just stepped in because the one before perished in said crisis.