I said it is PART of the reason and I didn't even specify to which extent. Big difference. Obviously one book by one author is not enough to fully shape an entire country, not even Mein Kampf or the Manifesto did that. However, it did provide a significant part of America's ruling class with a pseudo-intellectual justification for exploiting the lower and middle classes, which has worked splendidly. Today, they have amassed more wealth, priviledge and political influence than ever before, but still proclaim themselves victims of the welfare state (and even managed to convince the population to vote against their own interest on this). So who are these intellectuals/productives (very Randian assessment by the way, don't think a rich heir is more "productive" then a nurse, for example) willing to leave the US? They are in power under Trump, they are in power under Obama. Trump is one of them.
I'd go as far as to say that intellectuals @Craigie mentioned, who'd actually be willing to leave the US now because of the political climate, are not at all influenced by Atlas Shrugged. Quite to the contrary.