Health Care Choices for Seniors Act This bill amends title II (Old Age, Survivors, and Disability Insurance) (OASDI) of the Social Security Act to require the Department of Health and Human Services (HHS) to establish the Medicare Alternative Voucher (MAV) Program, under which a voucher may be used as a contribution into a health savings account and for the payment of enrollment premiums under a high-deductible health plan. HHS must establish a procedure under which an individual otherwise entitled to Medicare benefits may waive such entitlement and be automatically enrolled in the MAV Program. In addition, the bill amends the Internal Revenue Code to increase the amount of the deduction from gross income for health savings accounts by the amount of the MAV that is contributed to an individual's health savings account. The bill also suspends Medicare late enrollment penalties for an individual between ages 65 and 70.