He and his Veep would die before their terms are over, leading to an interesting 1944 election and a possible administrative crisis.
Willkie was a reluctant isolationist, and it would be hard to see him trying to avoid war with Germany. I'm less sure that he would push Japan into a corner--so WW2 might be against Germany only with US war entry in 1942/3, perhaps.
Question is, Willkie would die suddenly of the flu in 1944. What happens when the political campaign goes to pieces in the middle of a war?