The governor called McAllister's actions "an embarrassment."
The chairman of the Louisiana Republican Party, Roger Villere, has also called on the congressman to resign.
"Mr. McAllister's extreme hypocrisy is an example of why ordinary people are fed up with politics. A breach of trust of this magnitude can only be rectified by an immediate resignation," Villere said in a Thursday statement.
McAllister's office told the AP that "as of now, there are no plans of resignation."