It doesn't actually seem like an unreasonable claim, especially as there are so many contradictory definitions for "middle class", but I think we'd have a clearer picture if we could say, for example, "The median wealth voter in the US is 55% likely to vote Republican".
For context, here is what one source[0] says:
> Democrats have a huge advantage (63 percent) with voters earning less than $15,000 per year. This advantage carries forward for individuals earning up to $50,000 per year, and then turns in the Republicans’ favor — with just 36 percent of individuals earning more than $200,000 per year supporting Democrats.
> Interestingly, the median household income in the United States is $49,777 — right near the point where the Democratic advantage disappears and the Republicans take over.
[0] https://www.debt.org/faqs/americans-in-debt/economic-demogra...