I think that more attention should be paid to the possibility that Ike was absolutely sincere when he tried to persuade Nixon that taking a Cabinet post, and thus getting important executive experience, would be a better base for a successful presidential campaign in 1960 than remaining as vice-president. After all, the last sitting VP to be elected president (as opposed to becoming president by the incumbent president's death) was Martin Van Buren in 1836. Irwin F. Gellman makes the argument for Ike's sincerity in *The President and the Apprentice: Eisenhower and Nixon, 1952-1961,* pp. 311-313:
"Eisenhower's attitude toward Nixon in the second spot from Christmas 1955 until the end of April 1956 seemed baffling. The president never uttered an unkind or unpleasant word about his vice president, constantly called him a friend, and expressed his admiration. Yet he also doggedly held to the belief that Nixon should take a cabinet post and futilely encouraged people like Robert Anderson, who had no desire for the job, to seek the vice presidency.
"The president did not seem to understand that if Nixon did not run for re-election, opponents would perceive this as a demotion, damaging his future political prospects. It is possible that that the president had no better grasp of partisan politics than he had of politics within the faculty when he served as Columbia University president. Ike was a brilliant bureaucratic manager, a skill that he had learned in the Army and brought to the federal bureaucracy. The Army's way of grooming a promising young officer was to give him a succession of assignments, so that if and when he reached the high levels of command, he could call upon to wide range of experience. Nixon had done extremely well as vice president; now he could best burnish his credentials by accepting a new assignment.
"Nixon, acutely conscious of political actions, knew that a move from second in line to the presidency to a cabinet post, no matter how carefully or often it was explained, would look like a demotion. If such a move were even thought to be under consideration, his position would look tenuous. A relentless striver from high school onward, he felt strongly that if he were removed from the 1956 ticket, the public would conclude that he had been dumped. Partly out of vanity and, partly out of political savvy, he knew that it was not enough that he somehow maneuver his way onto the ticket. Leaders were drafted for their posts. Eisenhower had to pronounce him acceptable or even welcome, and possibly Nixon wanted to be asked.
"The president's physical problems may have contributed to the clumsy manner in which he dealt with the situation. The media reported, in minute and glowing detail, on his heart and his ileum, but not on the president's discomfort, the medications he was taking, or the extent of his inability to function during his recovery. In a meeting with New York Times columnist Arthur Krock on the afternoon on April 6, 1960, the president explained why he thought Nixon should have joined the cabinet. Ike "had no thought of trying to side-track Vice President Richard M. Nixon in 1956 when he suggested that Nixon might think a cabinet or equivalent post would better serve his aspirations to be nominated for President in 196o." He reminded Nixon that no vice president since Martin Van Buren had been elected president. Nixon considered the president's argument and rejected it. He thought that "an appointive post would be taken as a demotion" and also believed that because of the opportunities that the president had given him, his public approval would rise. While Ike considered six other Republicans who could fill the presidency, he concluded that "none had qualifications superior to Nixon's.".
"In the spring of 1970, Robert Anderson sat down for an oral history. He recalled that Ike had approached him on several occasions throughout 1955 for the second spot because he felt "that Anderson was the best qualified to run" and that the GOP would accept him. Ike never discussed Nixon, but he was not the president's "first choice." Even with Ike's flattery, Anderson refused to budge; he was not enticed to enter elective politics and remained a Texas Democrat until after the 1956 presidential election.
"In a conversation with Dillon Anderson, an Eisenhower National Security Council (NSC) adviser, on February 9,1968, the former president reiterated that "he was honestly trying to give Dick some good advice." When White House counsel Bernard Shanley recalled the drama over the 1956 vice-presidential ticket almost two decades after the fact, he said that the president sincerely felt that Nixon was "at a dead end with this job of Vice President." If he "were smart," he would take an equally significant cabinet post, "and then you'll have a real launching pad for the future." During two reminiscences, Attorney General Brownell held that Ike thought if Nixon wanted to run for the president, he needed "some administrative experience" like a cabinet position.
"If these opinions left any doubt as to the president's motivation, Milton Eisenhower, in the summer of 1983, recalled staying at the White House over the weekend when his brother talked to Nixon. Ike's admiration for him had increased with time. Ike offered Nixon a cabinet post because he did not see the vice presidency as "a good political springboard" for the top spot. According to his brother, the president never seriously considered another running mate in 1956. Milton stressed that while his brother might have preferred Robert Anderson, "he did not feel strongly enough about this to bring the matter to a climax.""
https://books.google.com/books?id=0UQJCgAAQBAJ&pg=PA311
It has to be said that Gellman has something of a pro-Nixon bias, and his statement that Ike "never uttered an unkind or unpleasant word about his vice president" is contradicted by Emmett John Hughes, who claimed that Ike told him, "The fact is, of course, I've watched Dick a long time and he just hasn't grown. So I just haven't honestly been able to believe that he is presidential timber.”
https://books.google.com/books?id=TvmRvRikXPMC&pg=PA240 Gellman dismisses this by noting that Ike denied saying it
https://books.google.com/books?id=0UQJCgAAQBAJ&pg=PA7 after Hughes published his account in late 1962. But this denial proves very little; it is hardly likely that Ike would *admit* in 1962 to saying such a thing about Nixon. And actually, Ike's denial was neither immediate nor totally unequivocal. "Eisenhower was upset by Hughes's memoir-—he regarded him as a turncoat—-and worried how his words would strike an already despondent Nixon, but he said nothing about it until early December, when the editor of the Augusta Chronicle tracked him down. He conceded that he might have said Nixon wasn't ready for the presidency in 1956, but that was not the same as saying that Nixon wasn't ready for the presidency, period..."
https://books.google.com/books?id=TvmRvRikXPMC&pg=PA240
(A more substantial objection, I think, is that if Ike *really* believed Nixon was not fit to be president, he would have dumped him from the ticket, regardless of any political embarrassment it would have caused--and Ike was certainly popular enough to withstand any such embarrassment. Instead, all he did was suggest that Nixon take a Cabinet position--accounts differ of what he offered, but the one I have seen most often is Defense--and when Nixon rejected the idea, kept him on the ticket.)