Via Zachary Goldfarb, here's a chart from the 2014 Economic Report of the President. It shows unemployment rates of various durations, and I've redrawn it a bit to scale everything to 100 in 2007. That gives you a clearer idea of what's going on. As you can see, short-term unemployment levels are nearly back to their 2007 levels and continuing to drop. Long-term unemployment, by contrast, is still three times its 2007 level.
For all practical purposes, long-term unemployment is now practically our entire unemployment problem.