Putting Veterans Funding First Act of 2013 - Authorizes the provision of advance appropriations for the following discretionary (under current law, medical care) accounts of the Department of Veterans Affairs (VA): (1) Veterans Health Administration Medical Services, Medical Support and Compliance, Medical Facilities, and Medical Research and Support; (2) National Cemetery Administration; and (3) Veterans Benefits Administration, Native American Veteran Housing Loan Program.
Authorizes the provision of advance appropriations for the following VA discretionary administration accounts: (1) general operating expenses, (2) information technology systems, (3) the Office of the Inspector General, (4) construction for major and minor projects, and (5) grants for the construction of state extended care facilities and veterans cemeteries.