Why Not Just Let The Bush Tax Cuts Expire?

Robert Reich asks a sensible question.  The Bush tax cuts went primarily to the wealthy, but they also provided some benefit the middle class.  Obama would like to eliminate the tax cuts for the wealthy but he wants to retain the middle class tax cuts.  If Obama were let the Bush tax cuts expire according to current law, he could simply propose new tax cuts for the middle class, and put the GOP in the position of voting against them.  Whats wrong with that strategy?