The couple declined to testify before Congress this week, but it now appears they are going to be subpoenaed and forced to appear as part of an investigation into how they were able to gain entry to the dinner.
"I think the lesson here is, when Congress wants to talk to you, you have to have to go eventually," said Schroeder.
Host Bob Schieffer, who believes the Salahis should be prosecuted, said that "for these people to cheapen something like that, I think it's a very serious offense." He asked Gavin if the story is going to die down.
"The story is going to continue to go on unless two things happen," Gavin said. "One, the Salahis speak, which I think will happen eventually, and two, the White House has kind of been kicking the can down the road a little bit…at some point, people are just going to have to put all their cards on the table and say, 'here's who's responsible.'"
Schieffer asked if White House Social Secretary Desiree Rogers' job was in trouble as a result of the snafu.
"I can't imagine that it's not in trouble," said Schroeder, who added that the administration might keep Rogers on to save face and not have to admit having made a mistake.
In general, she said, "you make a huge mistake like this, I think it's a fireable offense."
As for the Salahis, who have been portrayed as social-climbing fame seekers, Schroeder quipped that at this point, they might want to consider moving.
Watch the entire episode above.
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