The Right funded an alternative media and alternative academia (their think tanks) and developed a powerful narrative that explained why things seemed to be getting worse in the 1970s. They blamed things like stagflation on big government liberalism and labor unions. Unfortunately, many Democrats agreed that the era of New Deal liberalism had passed and accepted some aspects of the Reagan Revolution.
The Democrats are not alone in this. Most center-left parties in the industrialized countries moved to the Right by the 1980s. The center-left didn't have a coherent answer to the problems of capitalism in the 1970s and at the time many people saw theories like monetarism as correct or at least useful in dealing with the problems facing Western economies at the time.
Now we are at a point where the neoliberal order is breaking down and we are due for a swing back to the Left, I think, but unlike the 1930s there has been no resurgence in institutions like labor unions that provided the impetus for positive change. This is why I still think we need a stronger labor movement despite all of the problems that unions have now. Even in their weakened state I don't see any other institutions that are capable of presenting a narrative and program that working Americans need.
The Democratic Party always needed to be pushed in a more liberal direction, whether by unions or by the civil rights movement or whatever. That is not a knock on the Democratic Party, it is just the reality that political parties are only as strong as the institutions and movements behind them. A weakening labor movement has been a huge blow to the Democrats and this explains why the Republicans are so intent on destroying unions.