In what way was Ike such a Keynesian? He probably vetoed more spending than any other president.
He vetoed spending initiatives following the biggest spending glut in US history (at the time).
Ike was the guns to butter president. He converted parts of the military into peace-time agencies, like Interstate Highway System and NASA. He also coined the term military-industrial complex during a speech lamenting his inability to reduce military spending to Post-WWII-levels after the Korean War. Eisenhower also expanded New Deal programs and Social Security.
He was a moderate compared to the likes of LBJ, but by today's standards, he would be regarded as someone of the Keynesian persuasion. Goldwater certainly didn't think highly of his domestic agenda.