Veterans' Health Accountability Act - Directs the Secretary of Veterans Affairs (VA) to provide a voucher for the market price of the needed service for use at a non-VA facility for any veteran who has been denied health care at any VA facility on a timely basis (defined as one day for procedures and seven calendar days for tests).

Makes all veterans eligible for VA-paid care from non-VA facilities, and directs the Secretary of the VA to immediately prepare for the privatization of all VA facilities within one calendar year, if more than 10% of the Veterans Health Administration's budget goes toward such health vouchers.