Nah, it's a real bad look. If it had been Trump "extremist" or "fantastic" or something like that, it would be easy enough to brush off, but Trump "supporters" is easily interpreted as "anyone who voted or will vote for Trump" it's a bad look for the President to call 40% or so of Americans garbage.
"The only garbage I see floating out there is his supporters [or supporter's]. His demonization of Latinos is unconscionable and it's un-American."
I went and watched the video. He's pretty mush mouthed. He doesn't deliver any of it well. He gets pretty flustered right after the contested word and that could be meaningful. But I think it is important to note that he is obviously reading a telepromt. I feel pretty certain a professionally written statement being fed on a teleprompt wouldn't say Trump's supporters are garbage. If a White House speech-writer did mean that, the verb agreement is wrong and the immediate followup is about concepts, not people. It isn't written well. It doesn't make sense.
The White House says he said "supporter's", meaning the comedian himself. Then both sentences are about the comedian. The whole thing works in that model. I believe this is probably the truth.
Another model that works almost as well is if the teleprompt said "The only garbage I see floating out there is his demonization of Latinos. It's unconscionable and it's un-American." and Biden was talking along and thought it was going to say supporters and said it and then caught himself and tried to get back on the rails.
You can take your pick. But the version Republicans are playing really doesn't make sense.