Eisenhower's candidacy was opposed by many conservatives in the Republican Party. Without the Korean War to make military expertise the most relevant factor, the GOP campaign would have been focused entirely on opposition to the Democrats' economic policies. The natural standard-bearer for such a campaign would have been Robert Taft, who mounted a strong resistance to Eisenhower even in OTL. The absence of a Korean War could also result in a different Democratic ticket. Truman might remain popular enough to run for a third term, which he was entitled to do.
Without the Korean War, relations between the USA and the PRC would be less antagonistic, which would leave the PRC in a stronger position vis-a-vis its neighbors. In the first place, the ROC would most likely collapse due to a lack of American support. With a stronger PRC, and a resulting impression of east Asian stability, the US would be tempted to disengage from the region, to delegate the dirty work to the local superpower, and in particular to avoid direct involvement in Indochina. The US may treat Beijing as it treats Moscow, allowing the PRC to exercise a Soviet-style hegemony over its neighbors. Just as the US never considered invading Poland or Albania in OTL, in this timeline it would be a geopolitical impossibility for the US to invade Vietnam or Cambodia.
With a strong PRC locking up continental east Asia in its sphere of influence, US interventionism would have to find an outlet in the Middle East, South Asia, Africa, or perhaps the Americas. Instead of an unpopular war in Vietnam, there might be one in Biafra, Egypt, or Cuba. With the focus taken off the Pacific, these conflicts would have the potential to attract American attention and blow up into much larger wars. Just imagine if the United States sent troops to aid West Pakistan against India and Bangladesh.
