READING, Pa.—Joseph Nuñez at first didn’t like Donald Trump. “I couldn’t stand the guy. I didn’t like the way he spoke about Hispanics or people in general,” he said. But by 2020, Mr. Nuñez had become a fan of Mr. Trump’s style and priorities, and he voted in favor of giving the president a second term.

So did many other Latino voters in this working-class city who had once backed Democrats or, like Mr. Nuñez, had skipped elections altogether. Now, as political strategists continue to sift through the 2020 election results, the emergence of these newly Republican voters is setting off alarm bells within the Democratic Party.

Nationwide, Mr. Trump’s share of the Latino vote grew by 8 percentage points compared with 2016, an analysis by Catalist, a Democratic voter- data firm found earlier this year. New calculations by the firm find that while then-candidate Joe Biden won 61% of Latino voters, the shift toward the GOP meant that he carried the group by about 750,000 votes less than had Hillary Clinton, the Democratic nominee four years earlier.

That erosion is a danger sign for the party, given that President Biden’s winning margin in five states was less than 100,000 votes.

With Democrats defending narrow majorities in Washington—a loss in 2022 of just a few House seats and one Senate seat would give............