Fun fact: Short-term unemployment is actually lower than it was in 2007. Indeed, the percentage of the labor force that had been unemployed for five weeks or less didn't grow all that much during the economic meltdown.
There are ways to remedy this, and get that top category shrinking faster, and AEI's Michael Strain and Kevin Hassett and CEPR's Dean Baker have some interesting ideas. Direct job creation along the lines of the TANF Emergency Fund — perhaps the most effective part of the stimulus package — would probably help a lot, as would looser monetary policy through NGDP targeting or helicopter drops or negative interest rates.
But even if policymakers adopted those measures, some of the damage may be too hard to repair. Long-term unemployment leads to an erosion of skills, dissociation from the labor market and other forms of "scarring" that last for many, many years. Brad DeLong and Larry Summers argue convincingly that this and other forms of what economists call "hysteresis" (basically, the long-term damage produced by short-run recessions) could have permanently increased the unemployment rate even at times when the economy is operating at full steam, and could have reduced how fast the economy can even go when it's at full steam.