Several of the congressman's constituents say he should not resign, though Gov. Bobby Jindal and some other Republican Party leaders suggest he should step down.
McAllister beat the GOP establishment to win the seat in the first place, and there are questions about how a leaked security tape got to a local newspaper.
Voters say those circumstances are worth consideration, even if McAllister's actions are wrong.
The congressman won a special election last year. He says through a spokeswoman that he has no plans to step down.
Louisiana voters re-elected Sen. David Vitter in 2010 after he admitted a "serious sin" with prostitutes.
