Article VI of the U.S. Constitution describes treaties as "the supreme Law of the Land," along with the Constitution and federal statutes. U.S. Const. art. VI., cl. 2. Article II asserts that the President has the power to make treaties, "by and with the Advice and Consent of the Senate." U.S. Const. art. II, § 2, cl. 2.
There is a discussion of 1) the Constitution's Supremacy Clause, 2) Medellin v. Texas, 128 S. Ct. 1346 (2008), and 3) Foster v. Neilson, 27 U.S. 253 (1829) in section III ("Presumption for or Against Self-Execution?") of Curtis A. Bradley, Intent, Presumptions, and Non-Self-Executing Treaties, 102 Am. J. Int’l L. 540, 545-547 (2008).
Also, there is an analysis of the Medellin Court's reasoning in section B. 1. ("Chief Justice Roberts' Majority Opinion: Dualism and the Self-Executing Treaty Doctrine") of Ronald A. Brand, Treaties and the Separation of Powers in the United States: A Reassessment after Medellin v. Texas (was scheduled for publication in 47 Duq. L. Rev.).