Fiscally Responsible Relief for Our States Act of 2010

Fiscally Responsible Relief for Our States 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 November 30, 2010. Postpones the termination of the program until April 30, 2011.

Amends the Assistance for Unemployed Workers and Struggling Families Act to extend until December 1, 2010, 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 April 30, 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.)

Amends the Supplemental Appropriations Act, 2008 to apply to claims for EUC payments the terms and conditions of state unemployment compensation law relating to availability of work, active search for work, and refusal to accept work.

Requires a state to determine whether an individual is to be paid EUC or regular compensation for a week of unemployment by using one of four specified methods if: (1) an individual has been determined to be entitled to EUC for a benefit year; (2) that benefit year has expired; and (3) such individual has remaining entitlement to EUC for that benefit year, and would qualify for a new benefit year in which the weekly benefit amount of regular compensation is at least either $100 or 25% less than the individual's weekly benefit amount in such benefit year.

Amends the American Recovery and Reinvestment Act of 2009 (ARRA) to extend until January 1, 2011, the temporary increase in the federal medical assistance percentage (FMAP), under title XIX (Medicaid) of the Social Security Act (SSA), for any state with a certain unemployment increase percentage during the recession adjustment period. Requires the FMAP percentage increase for each state to be decreased: (1) for the second quarter of FY2011 to 3.2 percentage points; and (2) for the third quarter of FY2011 to 1.2 percentage points. Extends the entire recession adjustment period from December 31, 2010, through December 31, 2011.

Applies the FMAP percentage increases to Medicaid payments attributable to expenditures for eligible nonpregnant childless adults who would have been eligible for child health assistance or other health benefits under eligibility standards in effect as of December 31, 2009.

Appropriates additional FY2011 funds to the Department of Labor (DOL) Employment and Training Administration, Training and Employment Services for grants to states for youth activities, including summer employment for youth.

Rescinds the unobligated balance of each amount appropriated or made available under ARRA (except under title X: Military Construction and Veterans Affairs of division A) in order to offset the net increase in spending resulting from title I of this Act.

Makes related amendments to ARRA with respect to the supplemental nutrition assistance program (formerly food stamp program), and to the Internal Revenue Code to eliminate the advance refundability of the earned income credit (EIC) and to include in gross income certain amounts from taxable rollovers to Roth IRA accounts.

Rescinds $4 billion in appropriated discretionary unexpired federal funds.