The Commission on Presidential Debates has some advice for debate moderators this fall: leave the fact-checking to the candidates.

The Trump campaign is taking the same position. So are some former moderators, like Jim Lehrer, who has facilitated twelve presidential debates.

But many others -- including a wide array of journalists -- want the man moderating Monday night's debate, Lester Holt, to intervene if egregious lies are said on stage.

As a result, fact-checking, normally a pretty staid subject, is now the focus of a roiling debate in political and journalistic circles.

Hillary Clinton campaign aides are being outspoken about it: If moderators "close their ears to Donald Trump's lies, it will extend an unfair bias to Donald Trump. It will be the equivalent of giving him more time to speak," Clinton press secretary Brian Fallon said Sunday.

Related: Watch Brian Stelter's interview with Brian Fallon

But Janet Brown, executive director of the commission, which organizes the debates every four years, said on CNN's "Reliable Sources" that "I don't think it's a good idea to get the moderator into essentially serving as the Encyclopedia Britannica."

Once the fact-checking door is open, "I'm not sure, what is the big fact, and what is a little fact?" She added, "Does your source about the unemployment rate agree with my source?"

Trump campaign aides have staked out a similar position. Some of them say a pro-fact-checking stance is really an anti-Trump stance.

Trump campaign manager Kellyanne Conway responded to the Clinton camp's call for aggressive moderating by saying on ABC, "I really don't appreciate the campaigns thinking it is the job of the media to go and be these virtual fact-checkers."

This point of view stipulates that the candidates will challenge each other without the moderator stepping in. As Lehrer put it on CNN: "The moderator's job is to keep the flow going."

The counterargument goes like this: An actor or a robot could keep track of time. A journalist needs to represent the viewers and help make the truth known.

"We hate to leave absolute errors of fact on the table," former debate panelist Ann Compton said.

Related: 100 million? Ratings expectations for first Trump-Clinton debate are sky high

So is fact-checking a part of the job or not? On Monday, it will be up to Holt to decide.

The commission "asks independent, smart journalists to be the moderators and we let them decide how they're going to do this," Brown said.

Holt is well aware of the controversy. While he has not commented, one NBC staffer close to Holt said, "Lester is not going to be a potted plant." Another staffer seconded that sentiment.

The fact-checking debate revolves around this fact: Trump is unusually fact-challenged.

While both candidates have been criticized for shading the truth this year, top fact-checkers say Trump's lies are in a league of their own.

After reviewing every statement made by both Clinton and Trump for a week, Politico concluded that "Trump's mishandling of facts and propensity for exaggeration so greatly exceed Clinton's as to make the comparison almost ludicrous."

Trump even said last week that Holt is a Democrat, when in fact Holt is a registered Republican.

Related: How Lester Holt is getting ready for Monday's debate

The Clinton campaign wants the debate fact-checking to extend to post-debate TV broadcasts.

After Sunday's "Reliable Sources," Fallon tweeted, "in addition to need for moderator to do basic fact-checking," it is "equally important for post-debate assessments of Trump to not ignore his lies."

"Special measures are required this year," the campaign's communications director Jennifer Palmieri tweeted.

That tweet sums up a popular view about fact-checking, particularly among Democrats.

The other side is represented by people like Newt Gingrich, who tweeted, "How weak is Clinton that her campaign wants moderators to fact check Trump? Isn't that her job? Are they that afraid of Trump?"

Lehrer, the former moderator, took a more nuanced position, suggesting that thorough fact-checking will appropriately take place right after the debate, and will "go on and on and on right up to Election Day."

The moderators' job "is to facilitate the revelation of this man and Hillary Clinton as well. Who are these people? Who are they?"

Holt's NBC colleague Matt Lauer was widely criticized earlier this month for his handling of a "Commander-in-Chief Forum" with Hillary Clinton and Donald Trump. Lauer did not correct Trump on the Republican nominee's false claim that he had opposed the Iraq war.

Lauer's interviewing reignited an ongoing debate about fact-checking. Some commenters have pointed back to 2012, when former CNN anchor Candy Crowley fact-checked a statement by Republican nominee Mitt Romney about President Obama -- a controversial moment that seemed to benefit the president.

The moderators of the next presidential debate, CNN's Anderson Cooper and ABC's Martha Raddatz, have not weighed in on the subject.

But "Fox News Sunday" host Chris Wallace, who will moderate the third and final presidential debate, recently said he won't fact-check aggressively because "it's not my job to be a truth squad."