For background, see
http://www.unc.edu/depts/diplomat/AD_Issues/amdipl_13/sarantakes3.html
"The attack on Hagerty and the bloody riots of June 15 led many Americans to believe that that Eisenhower's trip would play a large role in determining the fate of Japanese democracy and orientation in the Cold War. Columnists Max Lerner and Harold Martin thought the President was putting his life in jeopardy with the visit. Many other journalists agreed that the President would be in danger. The trip was now a high-level gamble, but most observers thought Eisenhower had few options; the future of Japan was at stake and this was worth the risk he was taking with his life. 27 The editors of the Washington Evening Star disagreed and asked him to call off the trip. 'We think that Mr. Eisenhower, in the light of all that has happened, ought not to go to Tokyo.' 28
Eisenhower cancels Japan trip
As Americans debated the merits of the presidential expedition, Eisenhower began heeding the concerns he and others had and initiated efforts to cancel the trip. He had little concern about the future of Japanese democracy, but wanted to avoid being pulled into an internal Japanese dispute. Herter instructed MacArthur [Ambassador Douglas MacArthur II,
https://en.wikipedia.org/wiki/Douglas_MacArthur_II nephew and namesake of the general--DT] to meet with Kishi and tell him that unless he could guarantee the President's safety, the Prime Minister should request that the President delay his visit until another time. The ambassador did as instructed and Kishi stalled; his political survival was at stake. But the police had informed him that there was no way they could promise with a hundred percent certainty that there would be no attacks on Eisenhower; guarding the 11.6 mile route between the airport and the palace was beyond their resources. After the riot of June 15, Kishi had to admit defeat and formally requested that the President postpone his visit. 29"
Let's say Eisenhower (with Kishi's agreement) follows the advice of those who said that, whatever the risks, he had to proceed with the trip--to do otherwise would be to surrender to mob rule, etc. Let's further suppose that despite the best efforts of the Japanese police, he is killed during the trip. Vice President Nixon becomes President Nixon, and the advantage of incumbency--especially as the successor to the martyred Ike--should enable him to defeat JFK in November. Or is it even certain that JFK will be his opponent? LBJ's argument that someone with greater "maturity", foreign policy experience, etc. than JFK is needed in such a dangerous world may be more persuasive to the Democrats than in OTL.
As for the consequences in Japan, Kishi's failure to protect Ike may seal his own political doom, but he was doomed in OTL already, and presumably the LDP wins the new elections at least as heavily as in OTL--probably more so, if Ike's assassin is linked with the Left.