John Delaney has spent more than a year toiling in the Democratic presidential primary vineyard, working on the assumption that there would be—or at least should be—a place for a centrist not named Joe Biden.

What he has found, he says, is a primary-season process that tilts toward candidates of the left, which, not surprisingly, is the direction the party has moved.

It’s less clear that rank-and-file Democrats are moving left in the same way. Mr. Delaney fears the party may be passing by such voters in the center as it moves toward 2020—or worse, from the party’s perspective, driving them toward President Trump.

“Democrats I talk to I would describe as problem-solving Democrats, meaning they want their elected officials to just get things done that improve their lives,” says Mr. Delaney, a former congressman from Maryland and, before that, a successful entrepreneur. “And so I kind of think of most Democrats as centrist in that regard. But this primary process, I think, has skewed the process to the left.”

The campaign Democrats set in motion for 2020, Mr. Delaney argues, “was nationalized way too early,” robbing some of the ability of the early-voting states of Iowa and New Hampshire to do their traditional job of winnowing the field. “And I think that has skewed the energy to the left.”