In one photo, Babeu is seen posing in front of a mirror in nothing but his underwear. In another, he has his hand inside the man's partially unbuttoned shirt.
By Saturday, the accusations were already taking a toll on the sheriff. With the Republican presidential primary in Arizona a little more than a week away, the campaign of frontrunner Mitt Romney announced that Babeu was quitting his role as its Arizona co-chair.
"Sheriff Babeu has stepped down from his volunteer position with the campaign so he can focus on the allegations against him," Romney spokeswoman Andrea Saul told TPM. "We support his decision."
The sheriff was also scheduled to hold a news conference at 12:30 p.m. local time in Arizona to further address the allegations, according to a statement from his office. The event is expected to be streamed live on azcentral.com.
The New Times identified the accuser only by his first name, Jose, citing his fear that the sheriff would try to challenge his immigration status.
Jose said he met Babeu through the dating website gay.com in 2006, before he became sheriff, according to the newspaper. Babeu was a police officer in the Phoenix suburb of Chandler at the time and was elected as sheriff of Pinal County in late 2008.
Beyond the romance, the newspaper also said Jose volunteered for Babeu's campaign, maintaining his websites and social media accounts.
They were apparently together during Babeu's fast rise to becoming a national figure in the fight against illegal immigration. The sheriff first burst onto the national stage in 2010 when he appeared alongside Arizona Sen. John McCain (R) in a now-famous television ad, calling on the federal government to complete "the danged fence" along the US-Mexican border.
More recently, Babeu has been a frequent guest for Fox News for immigration-related topics, including the ongoing Fast and Furious scandal. He has endorsed Mitt Romney in the Republican presidential primary, and touted as a co-chair of the candidate's presidential campaign in Arizona. He even recorded robocalls for Romney that went out to voters in Iowa last year.
Jose told the New Times, however, that their relationship went sour in just the past year when he began to suspect that Babeu was using a website for casual hookups. Jose said he began to lash out at Babeu with anonymous web postings, and that's when things really got ugly.
He said the sheriff sent a lawyer after him. The lawyer claimed Jose's immigration visa was expired and told him he faced possible deportation if he ever went public with the relationship.
Jose told the newspaper that he was going public now because he was tired of living in fear.
In an interview late Friday with the Arizona Republic, Babeu declined to discuss whether he had a romantic relationship with Jose. But he acknowledged knowing him and denied the accusations that he ever threatened him.
"That never happened," Babeu said, according to the newspaper. The rest, he said, he was going to keep to himself. "My personal life is exactly that."
Evan McMorris-Santoro contributed to this report.