How did Americans react to the invention of nuclear weapons and the rise of the Cold War?

Do you mean the invention of nukes by the Americans, or by the Russians et al?

Opinion when Truman dropped the bombs was almost totally in favor. They had been at war for ~4 years and were looking at another 2 years or so. Nukes seemed like a blessing, because they ended the war.

The idea of the Russians having nukes frankly increased the paranoia Americans already felt about Soviet spies. Nobody liked the idea that the Communists had nukes, and there was always the idea in everybody's mind that they'd be used, and everyone would die (Mutually Assured Destruction, or MAD).

So Americans liked the fact that the US had nukes, not so much Russians having them. Nukes make everyone nervous.

They received it with a grin