A former campaign staffer for Sen. John Ensign is confirming her involvement in an extramarital affair.

Daniel Albregts, a Las Vegas lawyer for the couple, says that Doug and Cindy Hampton confirm that they are the couple Ensign referred to during his news briefing Tuesday.

Albregts calls it unfortunate that the senator chose to air what the lawyer calls "this very personal matter, especially after the Hamptons did everything possible to keep this matter private."

The lawyer says the Hamptons will be ready and willing to tell their side of the story at some point in the future. 

Earlier Wednesday, Ensign stepped down as chairman of the Republican Policy Committee, the fourth-ranking GOP position in the Senate. He is not expected to resign from the Senate. 

Senate Republican Leader Mitch McConnell, R-Ky., confirmed the move Wednesday afternoon. 

"He's accepted responsibility for his actions and apologized to his family and constituents. He offered, and I accepted, his resignation as chairman of the policy committee," the Kentucky senator said. 

Sen. John Thune, R-S.D., is seen to be the odds-on favorite to replace Ensign in the leadership post, according to GOP Senate sources. 

Several reasons contributed to Ensign's decision to step down from his post, according to a Senate GOP leadership aide. They included the likelihood of a persistent media firestorm stemming from his admission Tuesday; growing irritation within the conference regarding other distractions; and the possibility that more damaging information could emerge regarding the affair. 

Sources told FOX News the admission was prompted by a blackmail threat. Two Senate Republican sources close to Ensign said a former employee had asked Ensign for money in what both sources described as a case of "extortion." 

The employee, Doug Hampton, worked in Ensign's Senate office, and his wife, Cindy Hampton, worked for Ensign's re-election campaign. Both ceased working for the senator shortly after the affair ended, the sources said, with Cindy Hampton receiving a severance package. The circumstances of Doug Hampton's departure remain unclear. 

Ensign expressed regret Tuesday for his actions. 

"Last year I had an affair. I violated the vows of my marriage," Ensign said. "It is the worst thing I have ever done in my life. If there was ever anything in my life that I could take back, this would be it." 

Ensign spokesman Tory Mazzola said the affair took place between December 2007 and August 2008 with a campaign staffer who was married to an employee in Ensign's Senate office, however, it wasn't immediately clear whether the Hamptons were the couple in question. Ensign, 51, said he would not mention the name of the campaign aide involved in the affair. He described the woman and her husband as good friends. 

"Our families were close," a weary-looking Ensign said. "That closeness put me into situations which led to my inappropriate behavior. We caused deep pain to both families and for that I am sorry." 

Ensign made it clear he did not plan to resign. Ensign did not participate earlier Tuesday in a Senate vote concerning the ailing travel industry, an unusual absence considering the topic's relevance in his home state. 

He took no questions from reporters at the news conference. 

Ensign's wife, Darlene, also released a statement about the affair. The two had been separated at the time of the affair. 

"Since we found out last year we have worked through the situation and we have come to a reconciliation. This has been difficult on both families. With the help of our family and close friends our marriage has become stronger," Mrs. Ensign said. 

The Ensigns have three children. 

Ensign was first elected to the Senate in 2000 and quickly rose through the GOP ranks. He chaired the GOP's Senate campaign operation in 2007 and 2008, and last year was named chairman of the Republican Policy Committee. The committee coordinates the GOP's legislative efforts in the Senate. 

Last month, Ensign traveled to Iowa for a speech organized by a conservative advocacy group, sparking speculation that he had an interest in possibly running for president. Aides said the visit was about staking out a leadership position within the GOP. 

Ensign has been a rising star among conservatives, speaking out against President Barack Obama's stimulus package, statehood for the District of Columbia and union-organizing legislation and in favor of gun owners' rights. Ensign has been a member of the men's ministry the Promise Keepers, a Christian ministry. 

He had been highly critical of former Sen. Larry Craig, R-Idaho, who served in Congress for a quarter-century when he was arrested in an airport bathroom sex sting. Ensign stopped short of urging him to resign but suggested strongly that he should. 

"I wouldn't put myself hopefully in that kind of position, but if I was in a position like that, that's what I would do," Ensign said. "He's going to have to answer that for himself." In the end, Craig served out his term. 

Ensign is the latest member of Congress who has acknowledged infidelity. Sen. David Vitter, R-La., is rebounding from being linked with a prostitute. 

Over the years, Ensign and Senate Majority Leader Harry Reid, D-Nev., have worked closely on issues affecting Nevada and have an agreement not to criticize the other publicly. 

"Senator Reid's thoughts are with Senator Ensign and his family at this time." Reid spokesman Jon Summers. 

Republicans lost eight seats last November under Ensign's campaign leadership, with one race, in Minnesota, still undecided. The losses put Democrats within one seat of having a 60-40 majority, enough to prevent the GOP from blocking bills and appointments if all of them vote together. 

Ensign is a veterinarian and adopted son of a Nevada casino mogul. He clearly was the most influential Republican in his state as the governor, Jim Gibbons, struggled with a horrendous economy and accusations of infidelity as well. 

FOX News' Trish Turner and Carl Cameron and The Associated Press contributed to this report.