Justin Weidner and John Williams of the San Francisco Fed attempt to estimate the increase in the unemployment rate due to structural factors. They find the increase is relatively modest:
What Is the New Normal Unemployment Rate?, by Justin Weidner and John C. Williams, FRBSF Economic Letter: Recent labor markets developments, including mismatches in the skills of workers and jobs, extended unemployment benefits, and very high rates of long-term joblessness, may be impeding the return to "normal" unemployment rates of around 5%. An examination of alternative measures of labor market conditions suggests that the "normal" unemployment rate may have risen as much as 1.7 percentage points to about 6.7%, although much of this increase is likely to prove temporary. Even with such an increase, sizable labor market slack is expected to persist for years.
In the past, the U.S. labor market has proven to be very flexible and recessions have not usually been followed by long-lasting increases in the unemployment rate. But, in the wake of the most recent recession, many economists are concerned that developments such as mismatches in the skills of workers and jobs, extended unemployment benefits, and a rise in long-term joblessness may have raised the “normal” or “natural” rate of unemployment above the 5% level that was thought to be typical before the downturn. Indeed, a few economists have gone so far as to argue that the rise in the unemployment rate to its current level of 9% primarily reflects an increase in the natural rate, implying there is little slack in labor markets and therefore little downward pressure on inflation. This Economic Letter examines evidence regarding changes in the natural rate of unemployment in the United States since the recession began. ...
Mounting evidence suggests that structural factors may have increased the “normal” rate of unemployment to about 6.7%. Much of this increase is likely to be temporary. In particular, the extension of unemployment benefits probably accounts for about half of the increase. But, even with a 6.7% natural rate, current and forecasted levels of unemployment imply that significant labor market slack will persist for several years. It is important to stress that each of the methods used to estimate the natural rate is subject to considerable error, especially given the limited experience of very high unemployment in the post-World War II U.S. economy. As the recovery proceeds, we should develop a clearer picture of the new normal rate of unemployment.
So, a large part of the problem is cyclical, not structural and it is expected that "significant labor market slack will persist for several years." That calls for more aggressive policy from Congress, but that is unlikely to happen.
The unwillingness of Congress to provide more help can be traced in large part to the shape of the budget when the crisis hit. With the tax cuts and the increase in government expenditures for wars and other things during the Bush administration, the budget was in poor shape even before the crisis hit. When the crisis did hit, the poor shape of the budget led to an initial stimulus package that was much too small, and there was very little follow up when it became clear that the initial stimulus was insufficient. Now, although the the economic limits have not been reached -- helping the unemployed would have little impact on the long-run budget problem -- it appears that the political limits have been reached and more help for the unemployed is all but out of the question. Thus, while the Bush tax cuts did very little to spur economic growth, they were costly, and those costs go beyond the hole in the budget caused by the cuts. The resulting budget problems also limited our ability to respond to the recession, and all of the additional struggles that households will endure because we were unable to give them the help they need are part of the Bush tax cut legacy.