Organ Mountains-Desert Peaks Conservation Act This bill designates specified lands in New Mexico administered by the Bureau of Land Management (BLM) of the Department of the Interior as wilderness and as components of the National Wilderness Preservation System. Such wilderness areas shall also be administered as components of the National Landscape Conservation System. The bill designates approximately 100 acres of specified BLM land in New Mexico as a potential wilderness area, upon which Interior shall permit only those uses already permitted. When specified conditions have been met, this area shall be incorporated into the Robledo Mountains Wilderness. The bill releases from further review for designation as wilderness the public land in Dona Ana County, New Mexico, administered by the BLM and not designated as wilderness. The bill withdraws the Potrillo Mountains Complex from the Potrillo Mountains Wilderness and closes a specified route from public access, making it available only for administrative and law enforcement uses, including border security. In implementing a management plan for the Organ Mountains-Desert Peaks National Monument in New Mexico, Interior shall include a watershed health assessment to identify opportunities for watershed restoration. Any land or interest that is within specified state trust land acquired by the United States shall become part of the monument. Interior shall convey to the state of New Mexico specified BLM land in exchange for specified parcels of state trust land within the monument.