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I've just done a quick search as I remembered similar. It looks like he hinted at it in a speech, and told advisors that he'd only serve one term, but then pulled back from it.
https://www.axios.com/2024/07/03/biden-campaign-democrats-pledge-one-term
The big picture: Biden never made an explicit public promise to serve
just one term — though Politico reported that he had privately told
advisers that he wouldn't run again. Between the lines: Biden's
campaign comments likely signaled that he was only running because of
who his opponent was, Anthony Fowler, a professor at the University of
Chicago's Harris School of Public Policy, told Axios."You could argue he's trying to kind of have it both ways. He's trying
to kind of tell people, 'Don't worry, I'm only running for one term,'
without ever actually explicitly promising that," Fowler said.
I don't know if this is a false memory. I'm sure Biden said in the 2020 campaign that he would be a one term President. But then got into power and thought, I quite like this, so am going to hang on.
Harris, not being Trump not good enough this time?