(CNN) -- White House social secretary Desiree Rogers will not be testifying at Thursday's congressional hearing about the recent White House security breach, Robert Gibbs said Wednesday.
"Obviously, there's an ongoing assessment and investigation by the Secret Service" into the breach that occurred during the Obama administration's first state dinner, the White House press secretary said at his daily briefing. "We are working with and ready to work with anybody that has questions on that."
But, Gibbs added, "based on separation of powers, staff here don't go to testify in front of Congress. She will not be testifying in front Congress."
The couple accused of showing up uninvited to last week's dinner for the Indian prime minister insists that they didn't crash the party, but the White House disagrees.
Lawmakers will try to get to the bottom of the saga surrounding Tareq and Michaele Salahi on Thursday, if the couple testifies before the House Committee on Homeland Security as the panel investigates the apparent security breach.
As of Wednesday, the couple had not declined the invitation to testify, according to the office of Rep. Bennie Thompson, chairman of the House committee.
"Our goal is to try to get as much information about what occurred at this state dinner as possible and how this security breach happened. The White House should be the most secure home in America. And this breach brought a real vulnerability to light," Thompson, D-Mississippi, said on CNN's "The Situation Room."
The director of the Secret Service, Mark Sullivan, also has agreed to testify, according to the House Homeland Security Committee.
The Salahis, who are aspiring reality TV stars, not only made it through the checkpoint but also had their pictures taken with President Obama, Vice President Joe Biden and Indian Prime Minister Manmohan Singh.
The Salahis answered questions about the controversy for the first time on NBC's "Today" show Tuesday. Appearing with his wife, Tareq Salahi said the two "did not party-crash" the state dinner.
"We were invited, not crashers. And there isn't anyone that would have the audacity or the poor behavior to do that," he said.
Yet Gibbs said Tuesday that the Salahis were not on an invitation list of guests.
"If your name is not on an invitation list and you show up, in my book, that's called crashing," he said on CNN's "American Morning."
"The president was concerned about the security breach here, as was the Secret Service," Gibbs said. "The Secret Service is evaluating their procedures."
On the "Today" show, Gibbs was asked about a report that the Salahis had an e-mail exchange with a Pentagon official and believed that hey had an invitation.
"I think if you ask the Salahis directly, they were not on a list here at the White House. Their name was not in a security tower in order to get into this secure complex. And they had been told on a number of occasions that they did not have tickets for that dinner."
In a statement CNN obtained, Defense Department official Michele Jones denied that she helped try to get the couple on the list for the state dinner.
"I did not state at any time, or imply that I had tickets for ANY portion of the evening's events," Jones said in a statement that a White House official released.
"I specifically stated that they did not have tickets and in fact that I did not have the authority to authorize attendance, admittance or access to any part of the evening's activities. Even though I informed them of this, they still decided to come."
Jones is a special assistant to Defense Secretary Robert Gates and is the Pentagon's liaison to the White House. The Washington Post reported that the Salahis turned over copies of an e-mail exchange with Jones to Secret Service investigators.
In the "Today" interview, however, the Salahis suggested that there was no misunderstanding.
The Salahis also denied a report that they were uninvited guests at a Congressional Black Caucus dinner in September, saying a law firm had invited them and they were its guests at the dinner.
"Were we escorted out? Of course not. That's another gossip rumor," Tareq Salahi said, saying the story got started through a gossip column.
Yet a spokesman for the Congressional Black Caucus Foundation said Tuesday that the couple was asked to leave the event.
The Salahis -- who said NBC didn't pay them to make an appearance on "Today" -- have been characterized in some media reports as publicity hounds.
The couple said last week that they would appear Monday on CNN's "Larry King Live," but they canceled after CNN reported on several lawsuits involving the Salahis. The couple's publicist, Mahogany Jones, urged CNN to delay its report about the couple's legal woes.
The Secret Service is conducting a full investigation into the incident, and the Salahis said they are cooperating.
Jeffrey Toobin, CNN's senior legal analyst, said the couple could face criminal charges.
"When you think about trespassing, there is no more important place where one might trespass than the White House. So if they went in there under false pretenses intentionally, trespassing is definitely a possibility," Toobin said.
The Salahis told NBC that their lives have been "destroyed" by their notoriety.
"Unfortunately, we've been mischaracterized, you know, through the media and other paparazzi forums, and you know, our homes have been invaded, and it's been just devastating what's happened to Michaele and I," Tareq Salahi said.
CNN's Ed Henry, Kristi Keck, Jeanne Meserve, Martina Stewart and Brian Todd contributed to this report.