When you're writing a song of any kind, it helps if you know what happened. And in an alternate-history like this, there's more backstory than is going to fit in the song. So here's what happened.

I don't think that there's much doubt that the U.S. would have eventually won the war with Japan, even if a ground invasion had been required. And thus, the U.S. won the war in this scenario, some time in 1947. But the invasion of Japan was incredibly costly in terms of both American and Japanese lives, living up to the expectations that millions would be killed.

When the news came out after the Japanese surrender that Truman had held back the American super-weapon, because he felt it was too terrible to use, the public outrage was tremendous. The Democratic Congress (still so — they held control in the 1946 mid-term election with the war still on) impeached Truman and convicted him, removing him from office. By then, the order of Presidential succession had been changed, so Sam Rayburn became President. But a weakened America couldn't deal with the Berlin Blockade, so Berlin fell to the Soviets.

Meanwhile, charges of treason and dereliction of duty were brought against Truman for having kept the Bomb in his back pocket instead of using it. He was tried, convicted, and sentenced to be executed on the first Wednesday in November of 1948.

His pending execution was the subhead to the main — and accurate! — headline in that day's Chicago Daily Tribune:

"Dewey Defeats Thurmond"

And that's the rest of the story... :)