Dollar is too much popular and it has taken a large period to make his place in world economy so bitcoin will also require a hard struggle and a longer period to make a place resemble to dollar, but do not think that it will replace or not.
Not only popular, the dollar has more value since many economies depend on it. Not just the US. At this moment there is no currency that comes even close to compete with the dollar. Not even the EURO or Yuan. So no it's not possible, because the dollar (us economy) needs to crash at least 1 time.