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 determine to Congress whether excess general revenue Medicare prescription drug funding is projected for the fiscal year for which the budget is submitted. Treats an affirmative determination 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 made.

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 warning within 15 days after the budget submission to Congress for the succeeding year. States that such requirement 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 through September 30, 2013, as certified by the Board of Trustees of the Federal Supplementary Medical Insurance Trust Fund.

Expresses the sense of Congress that legislation submitted by the President in response to a warning 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 through September 30, 2013.

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