McAllister's office vowed that he intended to stay in office — for now. As for questions about whether he would stand for re-election in November, those were dodged.
Married and the father of five children, McAllister has not been seen in public since the video surfaced. He has missed several votes in the Capitol, including an important one on the Republican budget for the coming fiscal year.
His absence came as the state's Republican governor and party chairman sought to pressure McAllister to step down. Gov. Bobby Jindal called the congressman's behavior an embarrassment.
"Congressman McAllister 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," Jindal said Thursday.
Party chairman Roger Villere accused McAllister of "extreme hypocrisy" in a blistering statement that said "a breach of trust of this magnitude can only be rectified by an immediate resignation."
There was milder pressure from Washington, where House Speaker John Boehner said after talking to McAllister: "He's got decisions that he has to make." The nation's top Republican officeholder added, "I expect all members (of Congress) to be held to the highest ethical standards, and this is no different."
In an email Thursday, a spokeswoman for the congressman, Jennifer Dunagin, said that, despite the call for McAllister to step down, "as of now, there are no plans of resignation."
But asked about his plans beyond the current term, she said, "The congressman is not focused on re-election right now. His family is his No. 1 priority at this time."
No prominent Republicans have leapt to McAllister's defense since a video surfaced Monday showing him in the arms of Melissa Peacock, who was on his congressional payroll until resigning after the recording's existence became known.
The congressman had few allies within his party to which he could turn. Most of the GOP establishment had backed the state senator who was surprisingly defeated by McAllister in last year's special election.
McAllister, a political newcomer, put his family and his faith at the center of his campaign for Congress, appearing with his wife, Kelly, and their children in one commercial and vowing to "defend our Christian way of life" if elected.
In his statement, Villere said, "Mr. McAllister's extreme hypocrisy is an example of why ordinary people are fed up with politics."
"A video showing him engaged in conduct unbecoming a member of Congress, on public time, in a public office, with one of his employees, was the focus of the national press for days. I call on Mr. McAllister to put the interests of his nation, state and party above his own and step aside," Villere added.
The husband of the woman seen kissing McAllister, Heath Peacock, told CNN in an interview that McAllister has "wrecked" his life.
The two couples were friends, and both Peacock and his wife were listed as donors on campaign reports McAllister filed with the Federal Election Committee.
Although Boehner declined to discuss the conversation he had with McAllister, he has shown little tolerance in the past for wayward lawmakers. In 2010, Republican Rep. Mark Souder quickly resigned at the speaker's private urging after admitting to an extramarital affair with an aide in his office in Indiana.
For their part, Democrats were bystanders. The congressional seat appeared to be unwinnable for them, even if McAllister were to run again.
Whatever the pressure on McAllister, there is little or nothing the party or the congressional leadership can do to force him from office.
McAllister's political fate could be left to voters in the fall election. One resident of the congressional district suggested that was proper.
"We elected him, and it should be up to us to decide in November," said Pamela Nolan, a hospital pharmacist from Richland Parish.
Barrow reported from Monroe, La. Associated Press writer Brad Klapper in Washington contributed to this report.