Organ Mountains--Desert Peaks Conservation Act

Organ Mountains-Desert Peaks Conservation Wilderness Act - Designates specified areas in New Mexico administered by the Department of the Interior's Bureau of Land Management (BLM) as wilderness and components of the National Wilderness Preservation System (NWPS). Designates certain other BLM land as a potential wilderness area, which shall, upon publication of a notice in the Federal Register, be designated as wilderness and as an NWPS component, and incorporated into the Robledo Mountains Wilderness. Releases certain public land in Dona Ana County not designated as wilderness by this Act from further study for designation as wilderness. Establishes certain BLM-administered lands in the county as the Organ Mountains-Desert Peaks National Monument. Requires the development of a management plan for the Monument. Transfers administrative jurisdiction over specified acreage of the Organ Mountains Area from the Secretary of Defense (DOD) to the Secretary of the Interior to become part of the Monument. Requires the Monument and the wilderness areas designated by this Act to be administered as components of the National Landscape Conservation System. Amends the Omnibus Public Land Management Act of 2009 to adjust the boundary of the Prehistoric Trackways National Monument. Reserves specified land for use by the Secretary of the Army for military purposes. Requires the Secretary of the Interior to seek an agreement with the Commissioner of Public Lands of New Mexico for an exchange of certain BLM land in the state for parcels of state trust land.