Medicare Prescription Drug Savings and Choice Act of 2004 - Amends part D (Voluntary Prescription Drug Benefit Program) of title XVIII (Medicare) of the Social Security Act, as added by the Medicare Prescription Drug, Improvement, and Modernization Act of 2003, to direct the Secretary of Health and Human Services, for each year beginning with 2006, to: (1) offer one or more Medicare operated prescription drug plans nationally that offers qualified prescription drug coverage and access to negotiated prices, while allowing the plan to offer supplemental prescription drug coverage in the same manner as other qualified prescription drug coverage offered by other prescription drug plans; and (2) enter into negotiations with pharmaceutical manufacturers to reduce the purchase cost of covered Medicare part D drugs for eligible part D individuals, and encourage the use of more affordable therapeutic equivalents. Requires the monthly beneficiary premium charged under such a plan to be uniform nationally and for months in 2006 shall be $35 and for months in succeeding years shall be based on the average monthly per capita actuarial cost of offering the Medicare operated prescription drug plan for the year involved, including administrative expenses. Allows for adjustment of such premium amount in case of supplemental prescription drug coverage.