(CNN) For a time, Pete Buttigieg was on a glide path as he ascended in the Democratic race for president, emerging unscathed from the fall debates and raking in donations as he built a juggernaut in early states.

But this week, the 37-year-old South Bend, Indiana, mayor took his inevitable turn in the harsh glare of the 2020 spotlight. As a leading contender for the nomination, Buttigieg is now facing an avalanche of questions about his three-year stint at the prestigious management consulting firm McKinsey & Company , which has represented clients whose values do not exactly align with the agenda of a progressive Democratic candidate. Buttigieg has said a non-disclosure agreement prevents him from talking in detail about his work at the company.

Buttigieg's progressive rivals -- namely Sen. Elizabeth Warren -- have been more direct in recent days in their criticism of the Indiana Democrat. And online, Buttigieg's critics from the left have seized on and attempted to amplify his every perceived misstep.

Warren, who has fallen back in the polls as Buttigieg has risen, is seizing the opportunity to raise questions about the South Bend mayor's commitment to transparency.

On Thursday, Warren called Buttigieg to open his fundraisers to reporters: "I think that Mayor Pete should open up the doors so that anyone can come in and report on what's being said," she said during a gaggle after speaking at the IWillVote gala in Boston. "Those doors shouldn't be closed. And no one should be left to wonder what kind of promises are being made to the people who can pony up big bucks to be in the room."

She also said Buttigieg should disclose the names of his McKinsey clients, asserting that she had "done so from the time that I was still in the private sector." Buttigieg has said that the non-disclosure agreement he signed when he left in 2010 precludes him from detailing his work at the firm and he has asked the firm to release him in full from the NDA.

"I think that voters want to know about possible conflicts of interest. It is even more important that the candidates expose possible conflicts of interest right now," Warren said.

He faced more intense criticism from Chicago Mayor Lori Lightfoot during an event Iowa, who told him to his face that he should break the non-disclosure agreement.

"You said you can't talk about your work at McKinsey because of a non-disclosure agreement and you, I think said today that you got to honor your commitment to McKinsey," Loightfoot said to Buttigieg. "I'm asking you, shouldn't you break that NDA so that you have the moral authority and the high ground against somebody like Trump, who hides behind the lack of transparency to justify everything that he's doing."

When asked on Friday about Warren's criticisms by CNN's Jeff Zeleny, Buttigieg responded, "(it) could be a sign that we're winning the policy argument -- but I'll leave it to the analysts."

But the questions aren't going away, particularly as Buttigieg tries to forge a centrist lane within the Democratic field -- stirring up the antipathy of progressive activists who want to see an ideologically pure candidate like Warren or Bernie Sanders become the Democratic nominee.

Time at McKinsey under scrutiny

Buttigieg was already facing scrutiny for his thin resume -- with the exception of his experience as a lieutenant in the Naval Reserve who served in the war in Afghanistan. His Midwest rival, Minnesota Sen. Amy Klobuchar , pointedly argued this summer that a female candidate with his credentials never would have made it this far.

On the campaign trail this year, the South Bend mayor has generally downplayed his association with McKinsey as he tries to win the nomination within a party that has vilified the wealthy and cited big corporations as a major contributor to problems like income inequality.

Last month, Buttigieg told BuzzFeed's Henry Gomez that his stint at McKinsey is "not something that I think is essential in my story."

On Friday night, Buttigieg called on the firm once again to release his client list, provided a general description of the kinds of clients that he worked for, and said he mostly did research, mathematical analysis and presentations.

"I never worked on a project inconsistent with my values, and if asked to do so, I would have left the firm rather than participate," Buttigieg said in a statement to the press.

Buttigieg also told MSNBC Thursday that there wasn't any client at McKinsey who he regrets representing, and that he never represented a foreign government or a pharmaceutical company.

The focus on Buttigieg's work at McKinsey kicked into high gear earlier this week after the New York Times and ProPublica highlighted the firm's controversial 2017 recommendations to Immigration and Customs Enforcement agency that it should cut spending on food, medical care and supervision of its detainees.

That was enough to lead several immigrant rights groups to call on Buttigieg to return campaign donations from McKinsey employees.

He sought to turn his resume problem into a progressive credential Friday, telling New Hampshire Public Radio that while at McKinsey he "learned a lot about the amoral turn of mind that increasingly dominates corporate America."

"There are at least four times that I can think of in the decade that I left that company that I've opened up the newspaper and seen an infuriating story about something that they did with one of their clients, where it's clear that they didn't seem to feel any moral weight to the decisions that they were making," Buttigieg told NHPR in the interview that aired Friday.

He added that McKinsey's recommendation to ICE was "disgusting" -- "basically viewing cost-cutting as something that should extend to cutting basic needs for people who are being detained."

"It's a reminder that no matter how nice the people are in a business, or in corporate America," he said, "it's up to us as a democracy to set the rules, the left and right boundaries, the guardrails, for them to operate in, because the profit motive is not going to lead to ethical actions that don't lead to profit, unless we establish, as a matter of policy, what companies can and can't do."

But the idea that Buttigieg would use an NDA as a shield from talking about his own work at the firm drew the ire of the New York Times editorial board, which called on the South Bend mayor to be more transparent.

"This is not a tenable situation," the editorial board wrote this week. "Mr. Buttigieg owes voters a more complete account of his time at the company. Voters seeking an alternative to Mr. Trump should demand that candidates not only reject Mr. Trump's positions, but also his behavior — including his refusal to share information about his health and his business dealings."

Why Buttigieg joined McKinsey

Buttigieg's campaign biography on his website makes only a glancing reference to those three years at McKinsey, noting that he returned to the Midwest after Oxford and "took a job in the private sector, before realizing his heart was in public service."

He wrote in his memoir that at McKinsey "my classroom was everywhere -- a conference room, a serene corporate office, the break room of a retail store, a safe house in Iraq, or an airplane seat -- any place that could accommodate me and my laptop."

Buttigieg took the job after finishing his Rhodes Scholarship at Oxford, he said, because it offered a form of training about the private sector, and because he sensed "that the time had come to learn what wasn't on the page and get an education in the real world, if there was such a thing. Which is why I went to McKinsey."

At the firm, Buttigieg said he became an expert on North American grocery pricing, and worked on a handful of issues that were important to him including energy efficiency research to help mitigate greenhouse gas emissions in the US, as well as war-zone economic development to grow private sector employment in Iraq and Afghanistan.

He concluded however, "no matter how much I liked my clients and my colleagues, delivering for them could not furnish the deep level of purpose that I craved."

Pressed in the NHPR interview about what he had learned at McKinsey that could be helpful in government, he offered a safe answer: math and "how to organize teams to get work done."