There's no winning this argument with Republicans. Yes, it's a catch-22 for Obama. If the economy recovers, pukes will say it was the tax cuts, so they should be extended. If the economy tanks, pukes will say it was because there was UNCERTAINTY due to the tax cuts only being for 2 yeas, so they should be made permanent.
Of course, you can't argue that the crap economy and growing deficits during the Bush years were due to the irresponsible tax cuts and outsourcing of the middle class. They can time the collapse to the point where it seemed LIKELY that Obama would be elected, so therefore the markets collapsed due to pending socialism and "the largest tax increase in history."
The only way to win is to not play.