Health Savings Account Act This bill amends the Internal Revenue Code, with respect to health savings accounts (HSAs), to: (1) increase the maximum contribution limits for HSAs to match the sum of the annual deductible and out-of-pocket expenses permitted under a high deductible health plan, (2) allow individuals who receive primary care services in exchange for a fixed periodic fee or payment to participate in an HSA, and (3) permit HSAs to be used for fitness center memberships. The bill also allows a medical care tax deduction for periodic provider fees, including: (1) periodic fees paid to a primary care physician for a defined set of medical services or the right to receive medical services on an as-needed basis; and (2) pre-paid primary care services designed to screen for, diagnose, cure, mitigate, treat, or prevent disease and promote wellness.