How far any of the three veterans go in politics will be another test of the power of generational change, which propelled John F. Kennedy in 1960 and Bill Clinton in 1992. Millennials have now passed baby boomers as the nation’s largest bloc of voters, but they have few representatives in government.

“One of them, and I don’t know which one, is going to light a spark and get further than any of us can think,” Ms. Dunn said.

Part of the journey is coming up with ideas that separate them from Democratic orthodoxy. Mr. Moulton, for instance, said Democrats had to do more than simply oppose President Trump.

“I think there will be a reckoning that America goes through after Trump,” Mr. Moulton said. He added: “A lot of Democrats will self-righteously claim victory and try to lord it over the Republicans and say, ‘See, we were right all along,’ and that will be bad for the country. What we really need is Democrats who can be leaders and also uniters who can help the country heal after Trump.”

Each of the men frames an appeal that they believe will play to party strengths on the coasts and in urban areas, but also in the traditional Midwestern battleground states.

“The Republicans have actually done a good job of tapping into the anxiety people are feeling,” Mr. Moulton said. “But it also shows that Democrats have tremendous potential in places that people are hurting by showing a real path forward.”

Mr. Kander, who lives near Kansas City, raised a common worry in the Midwest, that its young people do not return to their hometowns because they see so little opportunity.