“Our population is so young that most of the people are in the 40-and-under category,” Matt Barreto, a founder of the polling firm Latino Decisions, said in an interview. “So in the aggregate he is doing really well” among Hispanic voters.

Indeed, Mr. Sanders remains far more popular among younger Latino voters than among older ones. But he now runs a strong second to Mr. Biden even among Latinos over 50, pulling 21 percent of their votes, according to a Pew survey released on Thursday. All of the other Democratic candidates poll in the single digits with this group.

“He came out of the 2016 election with a lot of following,” Mr. Barreto said. “When 2020 started, he was already a known quantity. But that by itself was not going to get him all the votes. He’s brought a number of high-level staff onto his campaign and he has people in senior leadership positions, and they are pushing the campaign to engage more in Latino outreach. That is paying off.”

It’s not just happening in Texas and California, and Latinos are not the only voters of color supporting Mr. Sanders to a significant degree. A national CNN poll released last week found Mr. Sanders pulling 30 percent of all nonwhite voters to Mr. Biden’s 27 percent.

A Monmouth University poll last week and the Pew survey were a little less kind to him than CNN’s poll, but those two still found him trailing Mr. Biden by just eight points among Democratic voters of color nationwide. (Monmouth polled those likely to vote in a primary or caucus, while Pew looked at all registered voters.)

The Democratic Party’s white electorate has grown markedly more liberal over the past two decades, but African-American and Hispanic Democrats — who now make up roughly two-fifths of the party’s membership — still tend to identify as moderate or conservative, according to years of Gallup data.

This would seem to present a challenge for Mr. Sanders, whose policy proposals favor an expansive agenda to fight poverty and climate change, and who draws some of his most solid support from voters who identify as very liberal.