Medicare Prescription Drug Cost Containment Act of 2004

Medicare Prescription Drug Cost Containment Act of 2004 - Directs the Secretary of Health and Human Services, on the same date on which the President submits a budget to Congress, to submit to Congress a determination as to whether there is projected to be excess general revenue Medicare prescription drug funding for the fiscal year for which the budget is submitted, and if there is an affirmative determination it shall be treated as a Medicare part D (Voluntary Prescription Drug Benefit Program) funding warning in the fiscal year beginning on October 1 of the year in which the determination is submitted to Congress.

Amends Federal money and finance law, as amended by the Medicare Prescription Drug, Improvement, and Modernization Act of 2003, to direct the President to submit to Congress proposed legislation to respond to such a Medicare part D funding warning made in a year within the 15-day period beginning on the date of the budget submission to Congress for the succeeding year. Provides that such amendment shall not apply if, during the year in which the warning is made, legislation is enacted which eliminates excess general revenue Medicare funding for the period beginning with the fiscal year for which the determination is made and ending on September 30, 2013, as certified by the Board of Trustees of the Federal Supplementary Medical Insurance Trust Fund not later than 30 days after the enactment of such legislation.

Expresses the sense of Congress that legislation submitted pursuant to such amendment in a year should be designed to eliminate excess general revenue Medicare funding for the period that begins with the fiscal year for which the determination is made and ends on September 30, 2013.

Sets out the special procedures for House and Senate consideration of the President's legislative proposal in response to such warning.