One of the reasons that the Emperor decided to surrender was that on August 12 (after both the atomic bombings of Hiroshima and Nagasaki) the Allies, through James Byrnes' State Department, had communicated to the Japanese government that unconditional surrender would allow the Emperor to remain on the throne. This technically was not a concession, as the Allies had never demanded that the Emperor be deposed, but it was a diplomatic move that was crucial to Japan surrendering when it did. Hirohito later stated that had the Allies not guaranteed that his authority would be preserved as Emperor, he would not have called upon Japan to surrender. Edward Drea writes that, "Prince Asaka, Hirohito's uncle and the most hawkish of the royal clan, then asked [Hirohito], if we cannot preserve
kokutai, will the war continue, (
senso wo keizoku suru ka). 'Of course,' was Hirohito's blunt answer" (p 219). source:
https://www.google.com/books/edition/In_the_Service_of_the_Emperor/Rb3YvM8ZmC8C?hl=en&gbpv=1&bsq=of course.
On this basis I challenge the idea that any U.S. President who negotiated with Japan would have been immediately impeached for treason, as this did not occur when Truman did so in reality. As
@bguy points out, engaging in diplomatic negotiations with an enemy nation is not "treason" as defined in Article III Section 3 of the U.S. Constitution which states, "Treason against the United States, shall consist only in levying War against them, or in adhering to their Enemies, giving them Aid and Comfort." You could make an argument that when the Air Force dropped leaflets on Hiroshima warning its inhabitants on an impending attack, this constituted "aid and comfort" to the enemy (especially since the city housed a Japanese military base) yet no one tried to impeach Truman for this.
FWIW, my late grandfather served in the Pacific Theater as a U.S. naval officer during the closing months of the war. He later was stationed in Japan from 1945 to 1946 during the Allied occupation. I spoke with him about his war service in detail a few months before he died. While he believed that the usage of atomic bombs was necessary to defeat Japan, nothing he said to me that indicated that he wanted to "tar and feather" Harry Truman for allowing Hirohito to remain on the throne if it brought the war to a quicker end.