LADY LAKE, Fla. - Rick Santorum became annoyed at reporters today for asking him why he didn't correct a woman at a campaign event who called President Obama an "avowed Muslim."

"Why do you guys ask these 'gotcha' questions, like it's my job to go out and correct everybody who says something I don't agree with?" Santorum said to reporters after the event. "I don't think it's my responsibility. Why don't you go out and correct her? It's not my responsibility as a candidate to correct everybody who makes a statement that I disagree with."

The woman told Santorum that Obama is not "legally" the president, that he "totally ignores" the Constitution, and that "he is an avowed Muslim." She asked Santorum why Obama is still president, and the candidate responded by saying, "I'm doing my best to get him out of the government right now."

"He uniformly ignores the Constitution," Santorum said, not correcting the woman on Obama's religion. "He did this with these appointments over the, quote, recess that was not a recess, and if I was in the United States Senate, I would be drawing the line."

Obama is a Christian, but hasn't been able to persuade many Republicans that he is, despite going to church and praising Jesus Christ publicly.

An August 2010 Pew poll showed 18 percent of Americans believe the president is a Muslim, up from 12 percent the month before he was elected.

During the 2008 campaign, a woman asked GOP nominee John McCain a question and called Obama an "Arab." McCain immediately corrected her, saying, "No, no ma'am, he's a decent, family man, citizen, that I just happen to have disagreements with on fundamental issues, and that's what this campaign is about."

Santorum told ABC News it wasn't his "responsibility" to "correct" every questioner that says something "crazy."

"There are lots of people who get up and say stuff in a town hall meeting and say things that I don't agree with, but I don't think it's my obligation, nor should it be your feeling that it's my obligation to correct somebody who says something that I don't agree with," Santorum told reporters.

At the end of his town hall at an American Legion Hall here, several Occupy protesters screamed, "Mic check" and "Stop the hate!" while throwing glitter.

He told reporters they "have the right to protest." They have interrupted several of his events, including his speech the night of the South Carolina primary, where he came in third.

Despite calls for him to get out of the race and back Newt Gingrich, Santorum was very clear after his event today that he intends to be in the race "long term" and he's looking beyond the primary in this state, which is on Jan. 31.

"We feel like we do as well as we can here and move on to the next state. We're focused on four or five primaries in the next week or so after Florida," Santorum said. "We're planning already for Super Tuesday states and investing resources in states there. So this is going to be a long campaign, and we hope to do well here, but we understand this is a very, very expensive state."

He added that "everybody realizes this race is going to change again in a week, change again in another week."

"If there's one thing we've seen about this race, it's unpredictable," Santorum said. "What you're seeing is, a lot of folks saying 'let's wait' and let this thing run out a little bit, see how the campaign is going, and that's what we're going to do."

He spent most of his speech, before taking questions from the audience, focused on health care and criticizing the president on his health care reform legislation. Most of the people there were senior citizens, a large part of  Florida's population.

The event space was only a half-mile away from The Villages retirement community, which has a large Republican population, and many of the people who attended Santorum's speech live there.