Apropos Ike, one of the biggest mistakes in analyzing the right is thinking that the right ever became 100% liberal, centrist, conservative, populist under Ike, Nixon, Reagan, &c.
This is especially so under Ike, who people think tag-teamed with Rocky to basically crush anyone who wasn't part of the old NE establishment. It's a nice story, but it's not really true.
Ike was very popular afterward, but he did not sweep the GOP primary in 1952. He instead ran neck and neck with Old Righty Robert Taft and had to play all sorts of backroom deals to get a majority of delegates.
He spent much of the primary "playing to the base" in a way that Goldwater fans would like and at least rhetorically was pro-smaller government.
Even so, many R Senators and Congressmen were not Ike men, and they often gave him trouble or killed reform ideas he had. National politics is not just the President.