Well, you asked who would run if Smith didn't and I provided an answer.
There people genuinely concerned that Smith and Kennedy would take orders from the Pope. They were mostly poorly-educated and white.
They were also protestant too. It was also one of the three things that shafted him in the election. He was a "wet" politician, or one that opposed prohibition, he was an Irish Catholic, and he was running against the party that seemingly brought prosperity. He literally chose one of the worst times to run.
No President ever paid attention either to the Pope or the Constitution.