Updated 2:48 p.m.

Former House Speaker Newt Gingrich helped revive his campaign -- twice -- with strong performances in GOP presidential debates.

The self-styled intellectual of the campaign, Gingrich has relied on expressions of support from debate audiences to convey strength in the gatherings, tossing red meat to the conservative audiences with attacks on the media and his Republican rivals.

And that helps explain why Gingrich, whose performance at a Monday night debate in Florida seemed subdued compared to recent appearances, is now threatening to skip any debate in which the audience is barred from participating.

"I wish, in retrospect, I protested when Brian Williams took them out of it, because I think it's wrong," Gingrich said this morning on Fox News, referring to the NBC Nightly News anchor, who moderated the bulk of the debate. "And I think he took them out of it because the media is terrified that the audience is going to side with the candidates against the media, which is what they've done in every debate."

Gingrich vowed to "serve notice" on future debate appearances, insisting that audiences be allowed to express support or opposition to candidates' answers. (A spokesman said Tuesday afternoon that Gingrich intended to attend all the debates, but would certainly protest rules barring audience participation.)

WATCH last night's entire NBC News/National Journal/Tampa Bay Times debate

The declaration wasn't necessarily a surprise, given the way in which Gingrich has made a conscious effort of playing to audiences at debates. Winning their applause by lobbing zingers at the media -- never unpopular among audiences -- is an easy way to improve perceptions of his performance, especially among television viewers.

He won his most raucous applause by assailing CNN moderator John King at a debate last week for asking a question of Gingrich about allegations from an ex-wife that the speaker had asked for an "open marriage" or threatened divorce.

“I am tired of the elite media protecting Barack Obama by attacking Republicans," Gingrich responded, winning a standing ovation from the audience, which wasn't barred from expressions of support.

Gingrich’s indignation with the “media” was such a hit, it was a major theme of his victory speech after handily winning the South Carolina primary Saturday night, as well as his round of interviews on the networks' public affairs programs the next morning.

Americans are “just sick and tired of being told what they’re allowed to think, what they’re allowed to say,” he told NBC’s David Gregory. “The highest, the most intense passion in both debates [in South Carolina] was a head-on collision about what the news media is doing.”

But Gingrich has also relied on the news media, too, to help advance his presidential bid. Like all campaigns and candidates, Gingrich uses press accounts to press his attacks on his rivals and to bolster his own claims on the stump.

When his campaign was being nearly crippled by the broadside attacks made by a pro-Mitt Romney super PAC in Iowa, the former speaker frequently pointed to fact-checking work done by news outlets to support his contention that the charges were bogus, an acknowledgment that the media can get it right, at least when it supports Gingrich's claims.

More importantly, the evidence suggests that Gingrich’s campaign has largely been sustained by his performances in the 17 debates that have been nationally televised thus far.  In exit polls released after voting finished in South Carolina, almost 90 percent of those voters interviewed said the two debates held in South Carolina were a factor in deciding which candidate to vote for -- and 42 percent of that group said they chose Gingrich, compared to 25 percent who picked Romney.  

The debates have been so integral to Gingrich's rise that he has pledged to challenge President Obama to a series of seven, three-hour-long Lincoln-Douglas style debates. Gingrich wins laughter and applause among crowds of supporters with this line, especially when he jokes that he'll allow the president to use a teleprompter, if Obama wants to.

It's smart politics, because Gingrich has made his ability to effectively debate Obama a central selling point of his candidacy. It plays well especially in a primary environment in which Republicans are longing for someone to take a fight to the president.

There's just one problem: It won't happen.

The Commission on Presidential Debates (CPD)is a nonprofit organization that has set the debate sites, moderators and rules for the general election in each cycle since 1988. They have already set the parameters for this fall's debates between Obama and his eventual GOP challenger. There will be three debates, held in October in Denver, Hempstead, NY, and Boca Raton, FL. The second debate will be in a town meeting format.

Gingrich probably won't be able to skip these debates if he's the nominee. But he might be reduced to protesting since, per the rules established by the CPD in every previous debate, the audience has been required to hold its applause through the duration of the meetings.

Tuesday night's debate focused primarily on foreign policy and national security. It featured light-hearted remarks about the GOP candidates' and moderator's names (Herman Cain accidentally referred to CNN's Wolf Blitzer as "Blitz"). And it shined the spotlight on a handful of audience questioners -- like former Bush administration officials Paul Wolfowitz and David Addington -- who played a key role in the United States' war in Iraq. 

But perhaps the most significant exchanges took place near the end of the debate on an issue not usually directly associated with foreign policy: illegal immigration. And they involved the latest GOP national front-runner (or co-front-runner): Newt Gingrich.

POLL: Where do you stand on illegal immigration?

"If you've come here recently, you have no ties to this country, you ought to go home, period," Gingrich said. "If you've been here 25 years and you got three kids and two grandkids, you've been paying taxes and obeying the law, you belong to a local church, I don't think we're going to separate you from your family, uproot you forcefully and kick you out."

When Michele Bachmann took issue with that statement -- equating it to "amnesty" -- Gingrich replied, "I do suggest, if you go back to your district and you find people who have been here 25 years and have two generations of family and have been paying taxes and are in a local church, as somebody who believes strongly in family, you're going to have a hard time explaining why that particular subset is being broken up and forced to leave, given the fact that they've been law-abiding citizens for 25 years."

And after Mitt Romney said that "amnesty" was a magnet for illegal immigrants, the former House speaker added, "I'm prepared to take the heat for saying let's be humane in enforcing the law without giving them citizenship, but by finding a way to create legality so that they are not separated from their families."

Gingrich's comments on illegal immigration are likely to delight Latino organizations, Democrats pushing for comprehensive immigration reform, and old Bush administration officials who tried to pass such reform into law yet failed. 

But support for a more "humane" policy on illegal immigration has knee-capped recent Republican presidential candidates. In the 2008 cycle, John McCain had not only supported comprehensive immigration reform; he co-authored legislation on the subject with the late Sen. Ted Kennedy. McCain's candidacy in the GOP primary suffered -- due in part to his views on immigration -- and he didn't truly recover until he disavowed his support for comprehensive immigration reform.

This cycle, Rick Perry -- who soared in the GOP polls after he announced his candidacy in August -- hit a brick wall after his GOP rivals (especially Mitt Romney) hit him on his support for allowing the children of illegal immigrants to have in-state college tuition in the state.

Will Gingrich be the latest Republican presidential candidate to trip over illegal immigration in a GOP presidential primary? We'll soon find out. 

Ironically, Romney himself appeared to support comprehensive immigration reform, according to a March 2006 article in the Lowell (MA) Sun. 

"I don't believe in rounding up 11 million people and forcing them at gunpoint from our country," Romney said, per the paper. "With these 11 million people, let's have them registered, know who they are. Those who've been arrested or convicted of crimes shouldn't be here; those that are here paying taxes and not taking government benefits should begin a process towards application for citizenship, as they would from their home country."

But his rhetoric has changed considerably since 2006.