Helping Responsible Homeowners Act - Directs the Federal National Mortgage Association (Fannie Mae) and the Federal Home Loan Mortgage Corporation (Freddie Mac) (government-sponsored enterprises or GSEs) each to carry out a one-year program providing for the refinancing of qualified single-family housing mortgages it owns through a refinancing mortgage (and for the purchase of and securitization of such refinancing mortgages) in accordance with this Act and the policies and procedures of the Federal Housing Finance Agency. Defines a qualified mortgage as one that: (1) is an existing first mortgage for purchase of, or refinancing another first mortgage on, a one- to four-family dwelling, including a condominium or a share in a cooperative ownership housing association, that is occupied by the mortgagor as principal residence\; (2) is owned or guaranteed by the particular GSE\; and (3) the mortgagor is current on payments due under the mortgage. Specifies the terms and conditions of a refi