Assanage's offer was always empty, given that the US isn't after him, at least not publicly. Now he contends that the US wants to get him in secret, though he's presented no evidence of this and of course one would have to question if they'd agree to a public deal for something secret.
Assanage is wanted by Sweden and the UK. Sweden for a sexual assault case, and the UK for skipping bail in that case. The US has not filed any charges against him, though I'm quite sure they don't like him. If he left the embassy he would be arrested by the UK and shipped off to Sweden. Or they might not send him off, since he's broken UK law by skipping bail and try him there for that crime, then ship him off once she's served his sentence.
So this was always a stunt.