In my opinion, the major impact of the Korean War came because people were simply tired of that war. That helped defeat Adlai Stevenson because he was too connected to President Truman in people's minds.
Because people were tired of the war, they wanted it to be over with. They equated Stevenson with Truman, who had not been able to bring the war to an end. They thought that Eisenhower would be more assertive and would get the war over with one way or another.
Ike helped make people think that by promising to go to Korea if elected -- this made it seem like he had some sort of plan without him having to say what that plan was.
Although Dwight D. Eisenhower might well have won the 1952 election without the Korean War, that war helped him be more certain of victory. The stalemate in the war and Eisenhower’s credibility as a hero from World War II helped to seal his victory.
By 1952, the war in Korea had become a stalemate. As such, it had become rather unpopular in the United States. Eisenhower used the people’s unhappiness over the war to his benefit. One of the major themes of his campaign was that the Democrats had mishandled the war. He charged that the Democrats had not been sufficiently prepared for a war. Because of that, he said, the war had ended up in a stalemate. He had credibility on such issues because of WWII. He promised to find a way to end the war if elected. This, too, helped make him more popular.
With Ike’s popularity, it is possible that he would have won the election regardless. The war in Korea, however, helped to make him more popular and thereby helped to ensure his victory in 1952.
The Korean War came as a shock to many within the United States political establishment and as the election of 1952 approached, Eisenhower (as the Republican Candidate) used their lack of preparation as a campaign issue. He railed against military and political weakness that would allow communism to expand and suggested that Truman and his cabinet had a large responsibility in the military lacking the ability to respond quickly and effectively to the North Korean invasion of South Korea.
Because much of the population wanted out of the war in the Korean peninsula and saw Eisenhower as a more likely candidate to be able to effect that change, it likely helped him win the election over Stevenson.
Consider the fact that a Democrat had been in the White House continually since 1932, a full two decades of one party control of the Presidency. In the second year of the Korean War, Truman's popularity was hitting record lows - 22% in February of that year.
Eisenhower was the winning commander of World War II, a moderate Republican and one who was seen by the public as someone who could break the deadlock in Korea and still handle the Soviet threat. He campaigned on that issue at the height of McCarthyism, appealing to peoples fears of communism at the time. He also promised that he would go to Korea if he was elected. This was much less common in those days as opposed to now.
The war itself was in stalemate, which made the 1952 election one that was about change as Americans looked for someone to take us in a new direction. Sound familiar? History repeats itself.