To get a rough quantitative estimate of the implications for the unemployment rate, suppose that the expansion of unemployment-insurance coverage to 99 weeks had not occurred and—I assume—the share of long-term unemployment had equaled the peak value of 24.5% observed in July 1983. Then, if the number of unemployed 26 weeks or less in June 2010 had still equaled the observed value of 7.9 million, the total number of unemployed would have been 10.4 million rather than 14.6 million. If the labor force still equaled the observed value (153.7 million), the unemployment rate would have been 6.8% rather than 9.5%.
See? If you assume that long-term unemployment is caused by extended unemployment insurance benefits, then removing unemployment insurance extensions solves the problem of long-term unemployment (and you get a pony!). This must be why he makes the big bucks. Magical thinking.
Suppose we make a different assumption. Let's assume that changes in consumer demand has an effect on the level of employment. If so, then the decision to not extend unemployment benefits would reduce demand for goods and services. Where will the jobs come from? Businesses are not going to expand their capacity or their workforce in the face of falling demand for their products. The only way that extending unemployment benefits could actually increase the unemployment rate above what it would otherwise be (other than just assuming it will, as Barro does) is to assume that the people receiving those benefits, rather than spending them on food and rent, use the checks to set fires to businesses that are currently employing people. This assumption has the advantage of actually leading to the conclusion that Barro reaches, without magic.
Update: cross-posted at Multiplier Effect.