One way or another they were children of the New Deal, the Great Depression, and the World Wars, so they were more in favor of big government than people are today. You aren't going to find Republicans today professing as much support big government as Nixon (or Ford or Eisenhower).
But the question and the objection is whether in practice, as opposed to rhetoric, the party or the country ever got very far away from that, even with Reagan. No Republican is going to propose or do the things that Nixon did or proposed -- wage and price controls, a guaranteed national income, an handgun ban -- but nobody is seriously going to "dismantle the New Deal" (whatever that might actually involve).
JFK was the man who destroyed America, without his election America would have survived, and would still be relatively healthy today, instead of being in an advanced stage of the process of it’s people being replaced.