His best chance there is that the US authorities have shown their hand by saying they want to charge him with espionage, which can carry the death penalty. As a general rule, we don't extradite European citizens to courts that might send them to be executed, and there would be outcry across the continent if the Swedish government made an exception for Assange.
How can the Americans charge him with espionage, if three million Americans already had privi to the same secrets? That has to be a bluff.