McAllister, a first-term Congressman who has five children and campaigned on family values and faith, was seen in a passionate embrace with scheduler Melissa Peacock in a video that surfaced earlier this week.
"As of now, there are no plans of resignation," said Jennifer Dunagin, a spokeswoman for McAllister.
“Congressman McAllister is focused on earning back the trust of those he has disappointed, and he reiterates his request for privacy for his family during this difficult period,” Dunagin said.
While earlier in the week, Dunagin said the congressman was considering asking the FBI to investigate the source of the video's leak, the plan seems to have been abandoned as calls for McAllister's resignation have grown louder.
"Congressman McAllister's behavior is an embarrassment and he should resign," Louisiana Gov. Bobby Jindal said in a statement Thursday. "He says he wants privacy to work on his issues with his family. The best way to get privacy and work on putting his family back together is to resign from Congress."
Louisiana Republican Party chair Roger Villere joined the governor in urging McAllister to step aside.
"Mr. McAllister's extreme hypocrisy is an example of why ordinary people are fed up with politics," Villere said. "A breach of trust of this magnitude can only be rectified by an immediate resignation."
In Washington, the condemnation was milder, and Speaker of the House John Boehner said McAllister "has a decision to make."
"I expect all members to be held to the highest ethical standards and this is no different," he said.