This was taught me in US History during my junior year of high school. My teacher was a major war nut, especially WW2, Korea, and Vietnam. Is any of that statement remotely true?
MacArthur did, indeed, ask the Joint Chief of Staffs for nuclear weapons during the Korean War. The Joint Chief of Staffs even approved his request, but though the weapons were transferred over, they were never placed under his command - a presidential order was required for actual deployment. He also submitted a list of "retardation targets" for nuclear weapons to the Joint Chief of Staffs as a strategy for winning the war, gave, at their request, a list of cities in northern China and Far East Russia for strategic nuclear bombing should the war ever get out of hand, and published posthumously a plan to win the Korean War by which 30 to 50 nuclear bombs would be dropped across the border of the Korean peninsula and China, which in his mind, would have created a radioactive no man's land that would serve as a buffer.
However, the popular idea that MacArthur was idiosyncratic in his exploration of nuclear weapons as an option against China is mostly a product of post-war politics. The fact is, the option was being widely debated within the Truman administration, and had the support of people such as General Curtiss LeMay and Director of Policy Planning Paul Nitze, in addition to MacArthur himself. Later, President Eisenhower threatened the Chinese with nuclear weapons unless they agreed to the armistice at the end of the Korean War, and even President Truman, though he publicly opposed their use, explored several option of using nuclear weapons to win the war up to about 1951. To be sure, most everyone in the US strategic command knew the value of wielding the Bomb as a political and military weapon - and in fact, so did the Russians and the Chinese, which is why they were so committed to getting the Bomb themselves, so as to neutralize the US advantage.
However, it should be said that MacArthur later denied that he ever recommended the use of nuclear weapons against China during the Senate Inquiry launched after his dismissal. He was specifically quoted as stating that "atomic bombing in the Korean War was never discussed either by my headquarters or in any communication to or from Washington." However, such claims were likely a product of the politics between MacArthur and Truman, at the time, since there is definite evidence that MacArthur did request the transfer of nuclear weapons to his command, and did discuss the possibility of its use with the Joint Chiefs of Staff. But the idea that MacArthur specifically recommended nuking the 12 largest cities of China during the Korean War is likely an exaggeration, and has no solid empirical basis.
As for MacArthur running for president after his dismissal, this claim is sort of accurate - he hoped to be nominated by the Republican party, though he didn't campaign very hard - and certainly the general disagreed with the Truman administration on its handling of the Korean War. But I do not believe he ever campaigned on the basis of dropping nuclear bombs in Chinese cities, especially since public sentiment in the US at the time was against the use of nuclear weapons on civilian targets.
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