Both Simpson and Cheney, the wife of former Vice President Dick Cheney, say the dispute centered on Simpson's earlier refusal to sign a football for Cheney's 15-year-old granddaughter at a recent fundraiser in Laramie.
The Cheneys' daughter, Liz Cheney, has galvanized Wyoming's political scene by seeking the seat of U.S. Sen. Mike Enzi, a Republican favored by his party's establishment. Simpson supports Enzi.
Simpson told the Casper Star-Tribune ( http://bit.ly/16qI6gq) on Tuesday that the disagreement with Lynne Cheney began a couple of weeks ago, at a fundraising event in Laramie for the University of Wyoming Art Museum.
Simpson said the Cheneys overheard his wife say during the event that the couple was backing Enzi. At the same event, Liz Cheney's daughter presented a football to dignitaries and asked them to sign it.
Lynne Cheney says the football was to be used to raise money for cancer patients. But Simpson said he declined to sign it after the teen said she didn't know if it was going to be used for campaign purposes.
"And that's when Lynne and (Liz's staffer) said, 'Do you think we would use it for a political fundraiser?' I said, 'I don't know. That has happened several times in my life.' And that obviously set off something," Simpson said.
The latest exchange took place before a fundraiser for the Buffalo Bill Center of the West.
"She just said, 'Shut up,'" Simpson said Tuesday of Lynne Cheney. "You can just read into it what you want to. I don't know what she meant. She was very intense."
Liz Cheney's campaign staff emailed a statement Tuesday night from Lynne Cheney, saying her exchange with Simpson was not about Enzi.
"It was about Al's blowup ... in Laramie, when my 15-year-old granddaughter asked him to sign a football to be used to raise money for cancer patients in Rock Springs," Lynne Cheney said in the statement. "Al was rude to my granddaughter, and I told him he was out of line. The topic was not Mike Enzi."
Liz Cheney's campaign, coming just a year after she and her family moved to Wyoming from Virginia, has struck some in this heavily Republican state as a presumptuous attempt to cash in on her famous name. Many in the Republican establishment have publicly sided with Enzi, the state's senior senator now running for his fourth term.
Enzi, the former mayor of Gillette and a former Wyoming legislator, succeeded Simpson in the U.S. Senate. Simpson said he didn't know if he would do any stumping for Enzi on the campaign trail.
"It's a deep-, deep-, deep-rooted friendship," Simpson said. "I didn't have that friendship with Liz."
But Simpson also said he's been friends with Dick Cheney for 45 years.
"I'm not out to hurt anyone," Simpson said. "That's not who I am. But I am a guy who states his case. And when I was asked about this, I said, 'I am sad, and I remain sad.'"
Information from: Casper (Wyo.) Star-Tribune, http://www.trib.com