The couple, Tareq and Michaele Salahi, have said they will invoke their Fifth Amendment right to refuse to answer questions.
Secret Service Director Mark Sullivan has said normal security protocols weren't followed and three uniformed Secret Service officers have been placed on administrative leave.
While the committee authorized subpoenas for the Salahis, it would not accept its top Republican's proposal to subpoena White House social secretary Desiree Rogers.
"I believe if we're going to get a full picture of what happened that evening, we have to have Desiree Rogers here," Rep. Peter King, R-N.Y. said. King said he is willing to work with the White House to come up with a way for Rogers to answer questions about the incident.
The Secret Service and the White House social office together developed the security plan for the state dinner honoring the Indian Prime Minister Manmohan Singh. Committee chairman Bennie Thompson, D-Miss., has been reluctant to subpoena Rogers -- an Obama political appointee -- because he maintains the Secret Service is responsible for security.
The Salahis said through their lawyer on Tuesday that the House Homeland Security Committee has drawn premature conclusions about the state dinner incident.
The Salahis have gone on national television and said they received an invitation to the dinner. But copies of e-mails they cited to buttress that claim show no such invitation was made.
The Salahis say they are cooperating with the Secret Service's criminal investigation.
Tareq Salahi has resigned from his position on the Virginia Tourism Authority Board.
Virginia's Department of Agriculture and Consumer Services is investigating a charitable polo event the Salahis sponsor.
In his resignation e-mail Monday to Virginia Gov. Tim Kaine and president of the tourism group Alisa Bailey, Tareq Salahi wrote, "unfortunate negative and tabloid type media" has made him a distraction to the tourism panel.