"I think any religious people would be outraged," Nosie said in a Wednesday interview. "The issue of it being a sacred site has never come to the forefront. That needed to be discussed."

Last year, the San Carlos Apache Tribe, Pascua Yaqui Tribe and Tohono O'odham Nation were among 20 Native American groups who sent a letter to Congressional leaders, protesting the land-swap bill. They argued it tramples on the religious rights of indigenous people. Nosie said it continues a pattern of "killing the identity of native people."

Opponents to the land-swap point out that the mine project could be undertaken without privatizing the land, which would ensure it would receive thorough oversight from federal agencies.

Pushing a land-swap through Congress is not the only option for the mining company to acquire the land, opponents say.

"Rio Tinto has yet to articulate any credible reason why a congressional land exchange is needed, versus the normal administrative processes," states the 2013 letter from the Inter-Tribal Council of Arizona to Congress.

Administrative land exchanges are much more common than legislative land exchanges, says a 2010 policy brief from the University of Montana.