According to some economists, neither high unemployment nor large deficits will keep the economy from rebounding. How to make this a parallel sentence?

It's already parallel.

neither high unemployment (= conjunction + adj + noun)

nor large deficits (= conjunction + adj + noun)

To make this a parallel sentence, we can rephrase it as: "According to some economists, neither high unemployment nor large deficits will hinder the economy from rebounding."