Eisenhower was echoing the work of sociologist, C. Wright Mills, and his 1956 book, "The Power Elite". Hugely popular and influential, The Power Elite was a clarion call of sorts in the emergence of the New Left and related off-shoots. 

https://en.wikipedia.org/wiki/The_Power_Elite
https://en.wikipedia.org/wiki/C._Wright_Mills

If he was alive, Professor Mills would chuckle at the notion that Donald Trump was leading a vanguard movement against the power elite.