My intuition tells me that Bitcoin would see a surge, as it becomes a stronger pillar of monetary value that crosses country borders, similar to the dollar, but not tied to the US.
Often those whims can correlate to shockwaves in the economy or the policies of the US and China trying to stomp out miners or trading but fundamentally they aren't reflective of broad market ideas the way most major stocks are. Bitcoin is much more centralized than traded stocks because its economy is so small and the barrier to entry so high.
People keep trying to find the trends in bitcoin, but the active pursuit of trends is what motivates the dominant whales to avoid being predictable.
As word of this spreads, fewer people will be buying coins for fear of having their coins held by a soon-to-go-under exchange. Lack of demand will then drive exchange rates down.
I think we got a taste of what will happen with economic certainty in 2008: they'll print more money. And in a situation like that, people will want something with the supply algorithmically constrained like Bitcoin.
If nothing else: Even if Bitcoin's "value" stays constant, its value in terms of USD will rise as inflation occurs. I'm not sure what rational case one can make that it would lose value as faith in the US economy gets weaker.