Look, there's no doubt that Obama is left of the American political centre, which is why he's the left's candidate and why they'll do their best to try and show off his left-wing credentials to preserve their own intellectual integrity. I don't have an issue with that.
But let's call spades spades here. In a general, standard-definition context, he's most definitely not left of centre.
This reminds me why I found label debates so boring all those years ago