Like, did Wendel Wilkie mention it in his campaign at all? He was breaking a 150-year precedent. Was he too popular for it to matter?
There's been a few similar questions asked recently that you might find interesting to read whilst you wait for a specific answer to your question (just incase these previous threads don't fully answer your question):
"What was the reaction to FDR running for a third presidential term?" - asked on 26/4/15
"How was FDR's decision to run for a third term received by the Democratic Party? By his 4th election was there "Roosevelt Fatigue"?" - asked on 3/4/16
"Did Americans ever have an issue voting FDR for a third term considering he was breaking the traditional 2 term maximum policy?" -asked on 14/4/15
"Were many Americans upset when FDR was elected for a third and fourth term?" - asked on 15/4/14
Hopefully this helps :)