The committee plans to vote Wednesday to subpoena the couple to testify.
In a letter Tuesday, the Salahis' lawyer, Stephen Best, gave examples of what he said were the committee's premature conclusions.
Best cited District of Columbia Delegate Eleanor Holmes Norton's characterization of the Salahis on Nov. 30 as "practiced con artists."
Best also said that Chairman Bennie Thompson's chief oversight counsel told the Salahis' lawyers that if the couple did not testify at a Dec. 3 hearing, they would be viewed as modern-day versions of "Bonnie and Clyde."
"It is circumstances such as these for which the Fifth Amendment of the United States Constitution was designed to provide safe harbor," Best wrote.
The Secret Service is currently conducting a criminal investigation into the security breach; charges have yet to be referred for prosecution.
In identical declarations dated Dec. 7, the Salahis said:
"I am aware of statements made by certain members on the Committee on Homeland Security in which premature conclusions concerning my criminal liability have been made. ... The current circumstances warrant invocation of my Fifth Amendment privilege against self-incrimination."
Three Secret Service officers have been put on administrative leave after the security breach. President Barack Obama acknowledged that the system did not work as it should have, but he said the episode hasn't shaken his confidence in his protectors.
Secret Service Director Mark Sullivan has said that the security breach is his agency's fault but that the president was never at risk.