I hate to be pedantic but the poll you reference was in 2020 and Trump said that in May of 2021. I don't think it had a measurable effect on either party.
> Democrats' reduced confidence follows President Donald Trump's Labor Day announcement that a coronavirus vaccine could be ready in October, as well as subsequent news reports stating that Trump is eager to see a vaccine delivered before the election. Trump's accelerated timeline does not align with that of many government health experts, and this disagreement has raised concerns as to whether a vaccine distributed that soon would be effective and safe.
https://news.gallup.com/poll/321839/readiness-covid-vaccine-...
I'm not a Republican or a Democrat, I'm a scientist.