Tareq and Michaele Salahi released a statement Wednesday saying they have cooperated in interviews with the Secret Service and members of Congress and have nothing more to add, ABC News reported.
"They therefore respectfully decline to testify," the statement said.
Rep. Bennie Thompson, D-Miss., who chairs the Committee on Homeland Security, said he had requested the couple appear before the committee Thursday.
"If the Salahis are absent from tomorrow's hearing, the committee is prepared to move forward with subpoenas to compel their appearance," Thompson said in a statement.
He said the Salahis could provide valuable information about how they "circumvented layers of security at the White House."
ABC said it obtained e-mails between the Salahis and Michele Jones, a Pentagon official who was trying to get them tickets to an outdoor ceremony to greet Prime Minister Manmohan Singh, which was canceled because of bad weather, or to the dinner. Jones's final e-mail said she had not been successful.
The Salahis e-mailed Jones in the early morning after the dinner, saying they had gone to the White House gate to check and had discovered their names on the guest list.