According to Wikipedia, Lehman's 600 ship navy only required 16 post-essex class carriers. Given the controversy and cost around this, it's fair to say you would need a major POD to justify 20, most likely one that involves the emergence of a naval power with its own blue water, carrier capabilities. The Soviets got close to this by the mid 80s but barely close. And as a continental power, I am skeptical that they would have gotten much closer. Their carriers were predominantly ASW and never really an offensive threat to the US. Frankly, I think you need a POD pre-1942 - most likely earlier - where a legitimate naval power like Britain, France or Japan is an economic power and an enemy of the US. But that that point the butterflies are so crazy you can run with your imagination.
That said, what could the navy have wanted for a hot war? Presumably a 2-4 carrier task force for each likely hot spot - Eastern Atlantic, Western Pacific, Med, Indian/Persian Gulf, Caribbean, and Eastern Pacific. Give me 4 each for the Eastern Atlantic and Western Pacific. 2 each for the Med and Indian/Persian Gulf. That gets you to 12 carriers. Figure to 2 more carriers for the Caribbean, Eastern Pacific, and ad hoc situations as the conflict calls. That gets you to 14-16 carriers plus 2-4 undergoing overhauls and refitting. It gets you to 20 but you have to convince congress that those 4 carrier TFs cant be reduced to 3 and that all those theatres need carrier support simultaneously. Can the caribbean be supported by land based air craft and is a carrier required for the eastern Pacific where its mostly ASW operations? Will the Med and Persian Gulf each need 2 carriers immediately or can they clear one theatre first and then proceed to the next one?
I think you need a clear, offensive blue water threat to get this.