I think it's been well-established that at the time, they were talking about the $1400 top-up payments. That someone else latched onto, "No, we mean $2000 right now!" as a message isn't Biden's fault.
It's okay to suggest that the plan should be the full $2000 right now, which people like AOC have been suggesting for quite a while, but you can't put the blame for other people's misunderstandings on Biden.
So, stop arguing about "what it meant", and just make the case for the $2000 straight up. There's actually a good case to be made for that, and almost certainly more. The anemic response of the richest country in history has been nothing less than an international embarrassment, after all, but that's the sort of thing American Voters have decided to support for decades now.
If you can't convince people to support economic change now, after almost a year-long economic disaster that isn't the fault of any business or employee, you'll never convince them. So go for it.
Just stop whining about how you didn't understand the math two months ago, because that makes you look like a whiny loser.