Depends. I reckon if the heart attack is bad enough to make him resign, he'll probably do it straight away. This would leave Nixon as the encumbent and therefore, the money would be on him winning both the 56 GOP nomination without too much ranker and ultimately, the election.
That's what happens in my Fallen Leader TL (which I need to finish)-though in that case the heart attack kills Eisenhower.
If Ike rounds out his term, I still can see Nixon as having a strong advantage in obtaining the 56 nomination, though if Ike backs someone else (like Warren?), then I think that person will be favoured for it in the end. Whoever the GOP candidate is, they probably win Ike's second term in 1956-Eisenhower himself is popular and the sympathy from his resignation would give that a boost, plus the Dems were in for 20 years before 1953.