National Flood Insurance Program Extension Act of 2010 - Amends the National Flood Insurance Act of 1968 to extend the National Flood Insurance Program from September 30, 2008, through September 30, 2010. Reduces the total amount of notes and obligations which the Director of the Federal Emergency Management Agency (FEMA) may through FY2010, with the President's approval, issue to finance the Program. Deems the amendments made by this Act to have taken effect on May 31, 2010. States that, to comply with the Statutory Pay-As-You-Go Act of 2010, the budgetary effects of this Act shall be determined by reference to the latest statement titled "Budgetary Effects of PAYGO Legislation" submitted to the Congressional Record by the Chairman of the House Budget Committee, if such statement has been submitted prior to the vote on passage.