The biggest obstacle in the path of Democratic majorities is not demographics or public opinion; it's that the party has completely failed to motivate voters to engage in politics and turn out to vote. Low-income Americans and Millennials are the least likely to go to the polls; whereas middle and upper-income Americans and older Americans are significantly more likely. The former comprise the Democratic base and the latter the Republican one. We have a participation gap that we must overcome.
Millennials have bad turnout rates mostly because they are young. They are also much more racially diverse, and young Hispanics/Asians have the worst turnout rates of all. Young African American turnout was doing well under Obama, but I think that will probably stabilize at a lower rate again.
This isn't really a problem Democrats can solve. Political engagement of the youth slid a long, long time ago and neither party has truly solved it, and that is because I think fundamentally increasing the level of attention paid to elections requires a sea-change in the way we raise and teach children about the society they live in, and what their place in it is. That being said, I think Democrats just happened to come to rely on these voters a lot more once they diversified, and thus suffered even worse turnout as a result. However, I would note, that in the past 3 presidential elections, youth turnout has been relatively good, all things considered.
The only tried-and-true solution here is to wait for these people to grow up some more. The same dynamic that benefited both parties in the past will slowly lift Democrats up as boomers die off and Millennials start voting more.