When she was asked how she calculated her $200 to $500 billion price tag, Ms. Williamson continued:

“If you did the math of 40 acres and a mule, given there was four to five million slaves at the end of the Civil War, and there were probably 40 acres and a mule for every family of four, if you did the math today, it would be trillions of dollars. And I believe that anything less than $100 billion is an insult, and $200 to $500 billion is politically feasible today because so many Americans realize there is an injustice that continues to form a toxicity underneath the surface, an emotional turbulence that only reparations will heal.”

Earlier in the debate, in a discussion about race in America centered on the water crisis in Flint, Mich., Ms. Williamson delivered an answer that showed her unconventional, and this time a bit more meandering, style, targeting President Trump and his recent attacks on politicians of color.

“My response is Flint is the tip of the iceberg. I was in Denmark, S.C., where there is a lot of talk about it being the next Flint. We have an administration that has gutted the Clean Water Act. We have communities, particularly communities of color and disadvantaged communities, all over this country, who are suffering from environmental injustice. “I assure you — I lived in Grosse Pointe, what happened in Flint would not have happened in Grosse Pointe. This is part of the dark underbelly of American society. The racism, the bigotry and the entire conversation that we’re having here tonight, if you think any of this wonkiness is going to deal with this dark psychic force of the collectivized hatred that this president is bringing up in this country, then I’m afraid that the Democrats are going to see some very dark days. “We need to say it like it is — it’s bigger than Flint. It’s all over this country. It’s particularly people of color. It’s particularly people who do not have the money to fight back. And if the Democrats don’t start saying it, why would those people feel they’re there for us. And if those people don’t feel it, they won’t vote for us, and Donald Trump will win.”

Her unorthodox approach has led to some viral moments for her fledgling campaign, such as saying in the debate last month that the first act she would do as president would be to call Prime Minister Jacinda Ardern of New Zealand, challenging Ms. Ardern’s claim that her country is the best place in the world for a child to grow up.

In a quip that quickly became a meme, leading to celebrity impersonations and some global news media coverage, Ms. Williamson said, “I would tell her: ‘Girlfriend, you are so on, because the United States of America is going to be the best place in the world for a child to grow up.’”

But Ms. Williamson’s relative rise in voter interest, as seen in trending internet searches and social media posts, has also led to more scrutiny of some of her more unsubstantiated stances, particularly on medical issues.

In various books and social media posts, Ms. Williamson has sometimes derided depression and claimed that antidepressant medication is recklessly overprescribed. She has also maintained that there is a link between antidepressant medicine and suicide. The Food and Drug Administration has warned for years that some antidepressants may increase the risk of suicidal thoughts in people age 24 and younger, but notes that untreated depression is itself a major risk factor for suicide.