I have heard this saying a dozen times over the years. My father first told it to me that if JFK were elected, no more Presidents would be elected, as he would turn the USA over to the Pope, and we would be a Church State. They said this about Barak Obama, and about scared people not to vote for Jimmy Carter.
I was in Missouri during that time and was told by a co-worker that if JFK was elected the Pope would move into the White House.
Well, he hasn't left the office yet.