Pinal County Sheriff Paul Babeu, a Republican running for the nomination in Arizona’s 4th district, announced today he is gay and said he is stepping down as a co-chairman of the Romney for President campaign in Arizona. He also said he would continue his race for Congress.

Babeu, an immigration hard-liner running against Republican Rep. Paul Gosar in the new district, had been the subject of reports in the Phoenix New Times that he was having a relationship with an illegal immigrant and that he had threatened the man with deportation if the immigrant went public with their relationship.

Babeu, who gained notoriety nationally for appearing in a 2010 campaign commercial with Sen. John McCain (R-Ariz.), has been a steady critic of the Obama administration’s immigration policies. In the ad, in which the Senator famously said, “Complete the danged fence,” as he and Babeu walked along a stretch of the border, Babeu told McCain, “Senator, you’re one of us.”

That year McCain faced a primary challenge from former Rep. J.D. Hayworth, another immigration hard-liner who criticized McCain as soft on border security.

Babeu, in addition to running for Congress, had also been a volunteer co-chairman for the presidential campaign of former Massachusetts Gov. Mitt Romney. He told reporters at today’s press conference that he had stepped down from that position.

The Phoenix New Times story broke late Friday and spread quickly. In it, a man identified as “Jose” alleged that Babeu’s attorney and Congressional campaign manager, Chris DeRose, had threatened him with deportation or other legal action if he went public with the relationship. Babeu said he had at one time had a relationship with “Jose” and that the man had done volunteer work for his campaign website.

Babeu was in Washington, D.C., last week, and spoke to the annual Conservative Political Action Conference.

“This is about an abuse of power, a misuse of public trust and the continued use of official resources for personal and political gain,” Gosar said Tuesday about the accusations that Babeu threatened “Jose” with deportation.

Gosar also called into question the propriety of Babeu’s press conference: “Today he hosted a campaign press conference in uniform at the sheriff’s office with sheriff’s office employees, campaign staff and campaign volunteers intermingled.  It is as though he believes the rule of law does not apply to him.”

“It’s catastrophic…He’s screwed,” an Arizona Republican strategist not aligned with any of the campaigns said.

But DeRose described the charges as “absolute nonsense.”

“No one has ever challenged this person’s right to be here. This person is as legal as you and me, and we’ve never had any reason to believe otherwise.”

He also noted a “tremendous outpouring of support” for Babeu on his Facebook page.

Abby Livingston contributed to this story.