It's really weird to act like Biden didn't want the ban and was some hapless third party to all this when before they even had the vote he was saying he'd sign it.

Bills don't get an automatic veto override if enough people vote yes, and an override doesn't make him sign it. He signed it because he wanted to, and in doing so he put the Democrat brand on it. He could have made them hold another vote to actually override his veto and make it clear that he didn't want this, he could have spoken out against it in any way before the bill was passed and on his desk, but he didn't, and now that it's wildly unpopular for some reason the entire DNC is just: