“The problem is in Wyoming and in South Dakota, they think they need a wall,” moderator Chuck Todd commented. “And in Texas and in Arizona, they don’t.”

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“I know,” Brokaw responded. “And a lot of this, we don’t want to talk about. But the fact is, on the Republican side, a lot of people see the rise of an extraordinary, important new constituent in American politics, Hispanics, who will come here and all be Democrats.”

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Brokaw then appeared to cite the fear of racial mixing and a majority-minority nation expressed by some Americans.

“Also, I hear, when I push people a little harder, ‘Well, I don’t know whether I want brown grandbabies,’ " he said. “I mean, that’s also a part of it. It’s the intermarriage that is going on and the cultures that are conflicting with each other.”

He broke off to offer his own commentary. “I also happen to believe that the Hispanics should work harder at assimilation,” he said. “That’s one of the things I’ve been saying for a long time. You know, that they ought not to be just codified in their communities but make sure that all their kids are learning to speak English, and that they feel comfortable in the communities. And that’s going to take outreach on both sides, frankly.”

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The panel discussion continued, but a few minutes later, Yamiche Alcindor, the White House correspondent for PBS NewsHour, pushed back against Brokaw’s remarks.

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“I would just say that we also need to adjust what we think of as America,” she said. “You’re talking about assimilation. I grew up in Miami, where people speak Spanish, but their kids speak English. And the idea that we think Americans can only speak English, as if Spanish and other languages wasn’t always part of America, is, in some ways, troubling.”

Once she had finished speaking, Todd told viewers that he had grown up watching the PBS program “¿Qué Pasa, USA?” — “three generations, all Spanish, Spanglish, and all English,” he said — then wrapped up the show for the week. Almost instantly, clips of Brokaw’s comments began going viral on Twitter, where he was roundly criticized for seeming to imply that Latinos had a responsibility to try to blend in better.

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A number of critics pointed to Pew Research Center statistics from 2013, which showed that a majority of Hispanic adults in the United States — about 62 percent — either speak English or are bilingual. Others, including the website Latino Rebels, cited a 2017 Pew study that found that 34 percent of the country’s Hispanic population was born outside the United States, arguing that it was inaccurate to cast Latinos as newcomers. And some noted that multiple studies have found that Hispanic immigrants are assimilating as quickly as previous immigrant groups.

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Latino Victory, a left-leaning political action committee that seeks to elect Latino candidates, tweeted that Brokaw’s remarks “give credence to white supremacist ideology” and “have no place in our political discourse.” The National Association of Hispanic Journalists, likewise, offered a scathing rebuke.

“Assimilation is denying one culture for the other,” Hugo Balta, the organization’s president and a senior producer at MSNBC, said in a statement. “Hispanics are no less American for embracing their country of origin or that of their ancestors … being bicultural and bilingual is a strength in an increasingly multi-ethnic, multilingual society.”

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Meanwhile, some right-wing media personalities spoke up in Brokaw’s defense.

“What’s wrong with asking people who come to America to assimilate?” asked the conservative radio host Joe Walsh. “Nothing. Tom Brokaw is correct.”

A little after 6 p.m. Sunday night, roughly eight hours after appearing on “Meet the Press,” Brokaw responded to the backlash on Twitter. Writing that he felt “terrible” that his comments on Hispanics “offended some members of that proud culture,” he once again said that all sides needed to work harder to find “common ground.”

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That didn’t go over well, either. “If @tombrokaw’s intent was to apologize, this is not an apology,” wrote journalist Yashar Ali.

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Others were displeased with Brokaw’s backpedaling.

“Those aren’t comments that anyone needs to apologize for making,” tweeted conservative commentator Erick Erickson. “They’re truths people don’t want to hear."

At 9 p.m., three hours after his initial tweets, Brokaw offered another round of apologies and blamed the interruption on technical difficulties.

“I am sorry, truly sorry, my comments were offensive to many,” he wrote in an additional string of tweets, adding that he had “never intended to disparage any segment of our rich, diverse society which defines who we are” and thanking Alcindor for her rebuttal during the show.

The National Association of Hispanic Journalists remained unimpressed.