Rebuilding Local Business Act of 2010 - Amends the Small Business Act to designate as a HUBZone (historically underutilized business zone), for purposes of assistance under such Act: (1) an initial period rebuilding county; and (2) an extension period rebuilding county. Defines an initial period rebuilding county as a county, parish, or similar political subdivision: (1) for which the Administrator of the Small Business Administration (SBA) determines that the one-year unemployment rate is at least 120% of the one-year average unadjusted unemployment rate for the United States; (2) that is not a HUBZone or will cease to qualify as a HUBZone two years after such unemployment determination; and (3) during the three-year period beginning on the date of such unemployment determination. Defines an extension rebuilding county as a county, parish, or political subdivision: (1) in which the Administrator has made the above unemployment determination; (2) for which the above three-year period has ended; (3) for which the Administrator determines that the unemployment rate as of a specified date is at least 140% of the average unadjusted unemployment rate; and (4) for which such designation extends for an additional specified period after the three-year period.