In Washington, Democrats are grappling with what it means to be a minority party in the age of Donald Trump. In the rest of the country, populist followers of Sen. Bernie Sanders are mounting a sustained effort to answer the question from the bottom up.

In California, supporters of the 2016 presidential contender packed the obscure party meetings that chose delegates to the state Democratic convention, with Sanders backers grabbing more than half the slots available.

They swept to power in Washington state at the Democratic state central committee, ousting a party chairman and installing one of their own in his place. Sanders acolytes have seized control of state parties in Hawaii and Nebraska and won posts throughout the party structure from coast to coast.

Those gains come from an under-the-radar blitz in a debate over the future of the party following its bruising 2016 losses. While Democrats nationwide have put the focus on President Trump, the Sanders wing of the party has engaged in an intramural fight to remake the party in a more populist, liberal mold.

“It is absolutely imperative that we see a major transformation of the Democratic Party,” Mr. Sanders said in an interview last week. The party has “to do what has to be done in this country, to bring new energy, new blood.”