Unemployment Insurance Extension Act of 2010

Unemployment Insurance Extension Act of 2010 - Amends the Supplemental Appropriations Act, 2008 with respect to the state-established individual emergency unemployment compensation account (EUCA). Extends the final date for entering a federal-state agreement under the Emergency Unemployment Compensation (EUC) program through December 31, 2010. Postpones the termination of the program until May 31, 2011.

Amends the Assistance for Unemployed Workers and Struggling Families Act to extend through December 31, 2010: (1) federal-state agreements increasing regular unemployment compensation payments to individuals; and (2) requirements that federal payments to states cover 100% of EUC.

Amends the Unemployment Compensation Extension Act of 2008 to exempt weeks of unemployment between enactment of this Act and May 31, 2011, from the prohibition in the Federal-State Extended Unemployment Compensation Act of 1970 against federal matching payments to a state for the first week in an individual's eligibility period for which extended compensation or sharable regular compensation is paid if the state law provides for payment of regular compensation to an individual for his or her first week of otherwise compensable unemployment. (Thus allows temporary federal matching for the first week of extended benefits for states with no waiting period.)