Responsible COBRA, Unemployment, and Poverty Extension Act

Responsible COBRA, Unemployment, and Poverty Extension Act - 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 FY2010. Postpones the termination of the program until March 1, 2011.

Amends the Assistance for Unemployed Workers and Struggling Families Act to extend through FY2010 requirements that federal payments to states cover 100% of EUC.

Amends the American Recovery and Reinvestment Act of 2009 (ARRA) to extend through FY2010, premium assistance for COBRA benefits (health insurance continuation benefits under the Consolidated Omnibus Budget Reconciliation Act of 1985).

Prescribes a special rule for an individual who experiences a qualifying event related to a termination of employment on or after June 1, 2010, and before the enactment of this Act. Applies to all COBRA continuation coverage, including state continuation coverage programs, with respect to such individual rules similar to those in the ARRA: (1) extending the election period for, and the effect on, COBRA continuation coverage; and (2) requiring a notice of such action by the administrator of a group health plan.

Amends the Department of Defense Appropriations Act, 2010 to extend the use of 2009 poverty guidelines through FY2010. Prohibits the Secretary of Health and Human Services (HHS) from publishing updated poverty guidelines for 2010 until after such date.

Rescinds pro rata the unobligated balance of each amount appropriated or made available under ARRA (except under title X: Military Construction and Veterans Affairs of division A), so that the aggregate amount of such rescissions equals $27 billion to offset the net increase in spending resulting from this Act.