“I think it scares people,” added Gov. Michelle Lujan Grisham of New Mexico.

The comments were a striking criticism of the direction the Democratic primary is headed, as progressive candidates have pulled the field to the left at a moment when President Trump and Republicans are eager to paint them as extreme.

“We cannot become the party of the checklist,” said Ms. Raimondo, alluding to litmus tests on cultural flash points. She urged the 2020 hopefuls to resist proving their liberal credentials on every issue and instead focus on “economic security for everyday Americans.”

[These are the mistakes Democrats don’t want to repeat in 2020.]

The governors’ angst offers cautionary signs for the party. They are often the best-known elected officials in their states and usually are the de facto head of their state parties, which means they wield considerable political clout. And with many of the governors having been on the ballot last year, they also possess a grasp of what the general electorate wants from Democrats.

Most of the officials have yet to support any White House contender and have largely avoided intervening in their party’s primary. But in the aftermath of last month’s debates, when a number of candidates, for instance, favored decriminalizing illegal border crossings and offering federal benefits for undocumented migrants, the governors are taking their pleas public.

Gov. Gretchen Whitmer of Michigan, who won last year with a mantra of “fix the damn roads,” recalled the show-of-hands moments in the first presidential debates, which she said illustrated the party’s shift left but were so terse as to offer no context or explanation about the candidates’ positions.