Today, Mr. Trump is still seen about as unfavorably by most Americans as he was in 2016, so Democrats hope that putting forth a more popular candidate will help them secure a wider majority of moderate voters, paving their path to the White House. Indeed, moderates deeply disapprove of the job Mr. Trump is doing as president: 58 percent of all moderates expressed disapproval of him in an NPR/Marist poll last month, while just 35 percent approved.

“Once we get into the general, it’s going to be incumbent on Democrats to pick up the moderate voters necessary to defeat Trump,” Mr. Manley said.

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Political shifts

As the Democratic Party has moved to the left, moderate voters have followed the trend on issues like gun control, climate change and wealth inequality. But on other questions, such as military spending and abortion rights, they tend to hold decidedly less progressive views than their liberal counterparts.

This is particularly true when it comes to health care: By more than 20 points, they are less likely than liberal Democrats to say they would prefer a government-run health care system, a result that’s consistent across various polls. That helps explain why center-leaning candidates such as Mayor Pete Buttigieg of South Bend, Ind., and former Vice President Joseph R. Biden Jr. have refused to endorse a Medicare for all plan, which they fear could endanger their chances in the general election — and may not be necessary to capturing the Democratic nomination.

Still, pinning down voters can be hard at the fluid center of the ideological spectrum. “Some people are genuinely moderate, in the sense that on most issues they hold moderate positions,” William Mayer, a political scientist at Northwestern University who has studied swing voters, said in an interview. “There are some people who are moderates because they have relatively strong feelings about a lot of issues, but those issues kind of cancel out.”

What, then, would moderate voters actually like the next president to accomplish? By wide margins, Democratic primary voters tend to tell pollsters that they would prefer a candidate who will take a new and different approach from former President Barack Obama. But moderate and conservative Democrats are more evenly split, with much greater numbers saying they’d like to return to the way things were four years ago.

This is driven in part by black moderates’ allegiance to Mr. Obama’s legacy, pointing to a possible source of durability for Mr. Biden’s support among the crucial, African-American portion of his base.