California Desert and Mountain Heritage Act

California Desert and Mountain Heritage Act - Designates as wilderness: (1) certain Bureau of Land Management (BLM) lands in the Cleveland National Forest, to be part of the Agua Tibia Wilderness; (2) specified lands in the San Bernardino National Forest to be known as the Cahuilla Mountain Wilderness and the South Fork San Jacinto Wilderness and certain BLM land in such Forest as part of the Santa Rosa Wilderness; (3) certain BLM land in Riverside County, California, to be known as the Beauty Mountain Wilderness; (4) certain land in Joshua Tree National Park, to be part of the Joshua Tree Wilderness; (5) certain BLM land in the county as part of the Orocopia Mountains Wilderness; (6) certain BLM land in the county as part of the Palen/McCoy Wilderness; (7) certain BLM land in the county to be known as the Pinto Mountains Wilderness; and (8) certain BLM land in the county as part of the Chuckwalla Mountains Wilderness.

Designates certain lands in the Joshua Tree National Park as potential wilderness. Requires the Secretary of the Interior to manage such land as wilderness until it is incorporated into the Joshua Tree Wilderness (effective when the Secretary publishes notice that all uses of the land prohibited by the Wilderness Act have ceased or that sufficient inholdings have been acquired to establish a manageable wilderness unit).

Provides for access to the Cahuilla Mountain Wilderness by Indian tribes for traditional cultural and religious purposes.

Amends the Wild and Scenic Rivers Act to designate as wild, scenic, or recreational rivers specified segments of the North Fork San Jacinto River, Fuller Mill Creek, Palm Canyon Creek, and Bautista Creek in California.

Amends the Santa Rosa and San Jacinto Mountains National Monument Act of 2000 to include additional lands within the boundaries of the Santa Rosa and San Jacinto Mountains National Monument.