Trump says adding his face to Mount Rushmore would be a 'good idea.' It would likely be impossible

President Donald Trump tweeted Monday that he thought it would be a "good idea," to have his face ono Mount Rushmore but making any additions to the landmark – whether it would be to add the 45th president or any other person – is likely not possible without jeopardizing the existing structure.

Trump, who has floated the idea in the past of having his face on landmark, posted the tweet in response to a New York Times report that the White House reached out to South Dakota Gov. Kristi Noem to inquire about what would be involved in making the addition.

"This is Fake News by the failing @nytimes & bad ratings @CNN," the president tweeted Sunday night, linking to a CNN article about the Times report. "Never suggested it although, based on all of the many things accomplished during the first 3 1/2 years, perhaps more than any other Presidency, sounds like a good idea to me!"

That tweet immediately followed one featuring a photo of Trump standing before the Black Hills monument from a perspective that put his face in line with those of former Presidents George Washington, Thomas Jefferson, Theodore Roosevelt and Abraham Lincoln.

In response to Trump's denial, New York Times spokesperson Ari Isaacman Bevacqua told USA TODAY, "We stand by our reporting."

In June, Mount Rushmore National Memorial chief of interpretation and education Maureen McGee-Ballinger told the Sioux Falls Argus Leader, part of the USA TODAY Network, that it was not possible to add a fifth president to the monument.

"The rock that surrounds the sculpted faces is not suitable for additional carving. When Gutzon Borglum, the sculptor of Mount Rushmore died in 1941, his son Lincoln Borglum closed down the project and stated that no more carvable rock existed," McGee-Ballinger, whose office is part of the National Park Service.

She said a rock mechanics engineering firm that studied the structural stability of the sculpture found that "no other rock near the sculpted faces is suitable for additional carving." And the firm warned that additional work could create "potential instabilities in the existing carving."

In addition, Borglum chose those four presidents specifically "to represent the first 150 years of the history of the United States — the birth, growth and preservation of our country" – and "not to represent the individuals themselves."

She said the memorial represents the ideals and meaning for which it was founded without the addition of other figures.

"The National Park Service takes the position that death stayed the hand of the artist and the work is complete in its present form," McGee-Ballinger said. "Thus, to maintain both the integrity of the structure and the artist’s concept, there is no procedure for adding another likeness, the sculpture is complete."

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McGee-Ballinger said the Park Service is frequently asked about the possibility of adding another president. People have advocated for the addition of several presidents, including Ronald Reagan, Bill Clinton and Barack Obama.

The addition of any of those presidents, or Trump, would be certain to ignite a political firestorm and infuriate their critics. On top of the partisan uproar it would be sure to cause, it would also likely meet with objection from Native American leaders, who have long decried the monument because it was built on land given to American Indian tribes through the Fort Laramie Treaty of 1868 before being seized by the federal government less than a decade later.

The Times reported Saturday that a White House aide reached out to Noem last year to inquire about the process to add a new president's visage to the Mount Rushmore monument. The article cited an unnamed Republican official who heard the conversation.

According to the Times, when Trump arrived in South Dakota for his speech at the monument on the eve of Independence Day, Noem presented Trump with a four-foot replica of Mount Rushmore that included his face carved beside the other four presidents.

Noem said in 2018, during her campaign for governor, that when she first met Trump in the Oval Office, he told her, "It's my dream to have my face on Mount Rushmore."

"I started laughing," Noem said, thinking the president was joking. "He wasn't laughing, so he was totally serious."

A year earlier, during a rally in Youngstown, Ohio, Trump mentioned the possibility of adding his face added to the iconic cliff.

"I'd ask whether or not you think I will someday be on Mount Rushmore, but here's the problem: If I did it joking, totally joking, having fun, the fake news media will say 'he believes he should be on Mount Rushmore,'" he said. "So I won't say it, OK? I won't say it."

While Mount Rushmore may not be an option, Noem suggested another possibility when Trump mentioned his "dream" in 2018.

"Come pick out a mountain," Noem said she suggested, jokingly.

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Contributing: Tom Lawrence, Trevor J. Mitchell and Michael Klinski, Sioux Falls (S.D.) Argus Leader

This article originally appeared on USA TODAY: Trump likes idea of adding his face to Mt. Rushmore. Is it possible?