At Texas Southern University, a historically black university founded in 1927 and the site of last week’s Democratic debate, dozens of students, ages 19 to 23, differed on their top candidate. Senators Bernie Sanders of Vermont, Elizabeth Warren of Massachusetts, and Kamala Harris of California were among the favorites, as was one of the two Texans in the race, former Representative Beto O’Rourke.

For Mr. Biden, though, students carried mixed feelings. They respected his tenure as Barack Obama’s vice president, but implicitly rejected his campaign’s central premise, that the primary goal of Democrats in the 2020 election should be defeating President Trump.

They pointed to systemic problems they said the country must address, such as inequality, climate change and gun violence. The Democratic nominee, they said, should embrace progressive proposals like canceling student loan debt, the Green New Deal and gun buyback programs.