This myth was debunked decades ago, but I it's still repeated by some liberals. The myth is based on a deceptively cherry-picked quote from Eisenhower's book Mandate for Change. I quote from Dr. Robert F. Turner's book Myths of the Vietnam War (1972):
Another very popular myth — related to both the 1956 elections and the "Ho Chi Minh as George Washington" myth, is the "Eisenhower quote." As Senator Wayne Morse phrased it in 1965:
"Undoubtedly, the Viet Minh under Ho Chi Minh would have won such a free election. President Eisenhower declares in his Mandate for Change that all the experts he talked to in that period believed Ho would get at least eighty percent of the vote."
Other critics quote directly from President Eisenhower's memoirs. Felix Greene, for example, writes:
"The reason the US refused to allow elections was abundantly clear. No one who knew the conditions in Vietnam was in any doubt that, if elections were held, Ho Chi Minh would be elected by an overwhelming majority of the people."
He then (mis-) quotes Eisenhower:
I have never talked or corresponded with a person knowledgeable in Indochinese affairs who did not agree that had elections been held . . . possibly eighty percent of the population would have voted for the Communist Ho Chi Minh. (President Eisenhower, Mandate for Change, p. 372.)
It is instructive to compare what President Eisenhower really said with what Greene and the others quote:
I have never talked or corresponded with a person knowledgeable in Indochinese affairs who did not agree that had elections been held as of the time of the fighting, possibly eighty percent of the population would have voted for the Communist Ho Chi Minh as their leader rather than Chief of State Bao Dai. Indeed, the lack of leadership and drive on the part of Bao Dai was a factor in the feeling prevalent among Vietnamese that they had nothing to fight for. (Emphasis added to denote omissions).
Thus, (1) President Eisenhower was talking about an election which might have taken place in 1954, not 1956 (and the situation in both North and South Vietnam during this two-year period changed significantly to Ho Chi Minh's disadvantage, as will be shown shortly); and (2) he was talking about a contest between Ho and the French puppet Bao Dai. There is little question that Ngo Dinh Diem would have defeated Bao Dai by eighty percent of the vote, too. The "feeling prevalent among Vietnamese that they had nothing to fight for" was largely the result of having a choice between a French puppet and a Communist dictator, when the majority of Vietnamese really wanted a true nationalist. (pp. 32-33)