The United States Supreme Court case Army and Air Force Exchange Service v. Sheehan in 1981 revolved around the issue of whether or not federal instrumentalities, such as the Army and Air Force Exchange Service (AAFES), are exempt from state taxation. The AAFES had refused to collect a New Mexico gross receipts tax on sales made at its facilities within the state, arguing that it was immune from such taxes under federal law. However, Sheehan, representing New Mexico's Taxation and Revenue Department argued that this immunity did not extend to third-party contractors operating under AAFES' authority. The Supreme Court ruled in favor of Sheehan stating that while direct federal entities were indeed immune from state taxation due to Supremacy Clause protections, this immunity did not extend to private businesses conducting operations for these entities. Therefore, third-party vendors operating within AAFES facilities could be subject to state taxes without violating constitutional principles.

In the dissenting opinion for the case of Army and Air Force Exchange Service v. Sheehan, it was argued that federal enclaves should not be exempt from state laws unless there is a direct conflict with federal law. The majority's interpretation of "exclusive" jurisdiction as meaning immunity from all non-consensual state regulation was seen as overly broad by the dissenters. They believed this could lead to an unfair situation where businesses operating on these enclaves would have competitive advantages over those in surrounding areas due to differing regulations and tax obligations. Furthermore, they pointed out that such a blanket exemption could potentially shield criminal activities taking place within these territories from prosecution under state law.