Organ Mountains National Monument Establishment Act - Establishes the Organ Mountains monument in Dona Ana County, New Mexico, to comprise approximately 54,800 acres of public land in the county.

States that, the purposes of the monument are the conservation, protection, and enhancement of its cultural, traditional, archaeological, natural, ecological, geological, historical, wildlife, livestock, watershed, educational, recreational, and scenic resources for the benefit and enjoyment of present and future generations.

Directs the Secretary of the Interior, through the Bureau of Land Management (BLM), to manage the monument in a manner to conserve, protect, and enhance those resources.

Requires the Secretary to develop a management plan for the Organ Mountains monument.

Allows hunting and trapping in the monument.

Releases the Organ Mountains, Organ Needles, and Pena Blanca Wilderness Study Areas from further study for designation as wilderness and prohibits such Areas from any longer being subject to requirements under the Federal Land Policy and Management Act of 1976 regarding the status of their lands during the period of review and determination of such areas for preservation as wilderness.

Requires such monument to be administered as a component of the National Landscape Conservation System.