Northern Vietnam had a larger population than the south so it would probably use its greater numbers to win the vote for Ho, as has already been mentioned. Everyone knew this at the time and that's why the vote was never held IOTL. allowing the vote would make about as much sense from the American perspective as some kind of vote on German reunification would make for the USSR. For this to happen you need a serious lapse in judgment on Eisenhower's part or an earlier POD which makes the above untrue.
As far as the effects go. There is probably a conservative backlash if the vote goes through and republican cries about 'who lost Vietnam' that echo the fears about the PRC a few years previously.
and obviously no Vietnam war, which is a big butterfly whose effects have been discussed previously in many threads.
It would have been political suicide for Eisenhower to give the Communists vietnam on a silver platter.
You're assuming that the United States is populated by 21st century people with the benefit of hindsight. This is the height of McCarthyism, and Eisenhower would be very conscious of the fact that his predecesor's political career was ruined by the perception that he was soft on Communism and had given up China to the Reds (and nearly lost Korea as well). 1956 is an election year, and if Eisenhower wants a second term he knows he needs to seem touch on Communism.Only amongst the nitwits who Vietnam was theirs to ‘’give‘’ in the first place.The Viet-Minh had already taken Vietnam for themselves, and then got screwed at the peace-table.
So Ike may incur short term problems, but the long term sense in having Ho as an ''Asian Tito'' would become apparent. Particularly vis-à-vis Maoist China. If the USA public can understand the reasons for helping Tito they can swallow this.