In 1984, Ronald Reagan won a huge landslide victory, sweeping 49 states while running on an unapologetic conservative platform. In the wake of that humiliation, Democrats began to think about what they needed to do to retake the White House. One result was the Democratic Leadership Council, a cabal of moderate Democrats who eventually helped Bill Clinton win the 1992 election. Clinton practiced a strategy dubbed triangulation, in which he placed himself between liberal Democrats and conservative Republicans, tacking back and forth as required to remain in power.
The most important issues on which Bill Clinton turned conservative were trade, crime, welfare, and Wall Street regulation. In 1992 Americans were seriously freaked about the great crime wave (even though it had already crested and started to recede), and the every night the news was full of "wildings" and "superpredators" and speculation about whether crime would render cites like New York and Washington uninhabitable. Clinton's plans to jail more offenders and put more police on the street were among his most popular policies. As for welfare, even many liberals were unhappy about Aid to Families with Dependent Children, which provided subsidies targeted to single mothers at a time when everyone was worried about falling marriage rates, so Clinton was able to get liberal think tank types and Congressional experts to work with him on his reform. Wall Street deregulation looms very large in the wake of 2008, but I don't remember it being nearly as controversial as some of Clinton's other policies. The reform was sold as a necessary update to outdated 1930s laws that didn't even mention things like hedge funds that had become central to modern investing. So some update was obviously needed, and I am not sure how many people understood at the time how much dangerous deregulation was snuck into the law. NAFTA was certainly very controversial, but at that time all the economists (even Robert Reich and Paul Krugman) were sold on the orthodoxy that trade promoted growth, and their arguments overrode opposition from labor unions (which were then at their nadir of popularity).
Clinton's program seemed relatively successful against the backdrop of economic boom times, but really nobody liked it. Conservatives continued to hate Democrats on principle and liberals accepted Clinton's compromises only because the only alternative seemed to be a return to Reaganism. In the 1990s, liberals simply did not have the votes to win national elections.
What about now? Have things changed?
Certainly they have in the Democratic Party. Glancing at the primary results you have to think that if Bernie Sanders can get 45% of the vote, a more plausible New Deal candidate would be running away with the race. The belief among older Democrats that Clinton/Obama centrism is the best America can do is being elbowed aside by young activists who want a return to both the economic populism of the 30s and the race agitation of the 60s. It looks like Hillary is set to win this year's race, but the future of Democratic moderation is dim. Whether or not she becomes president, the Democratic party is sure to be pushed leftward. I venture to predict that the next Democratic presidential candidate after Hillary will be somebody much to the left of Obama and the Clintons.
As to how that candidate will do in the election, I have no idea. It certainly seems that most Americans want a change from the politics of the last 36 years, something that will favor ordinary people and do less for the rich. Whether a majority can be persuaded that Democratic Socialism is that new politics remains to be seen. For one thing, Democrats have not tried to raise taxes on people earning less than $250,000 a year, and ambitious social policies like free college or more expansive health reform will require it. If a Democrat can win the White House on a platform of tax increases for everyone, a new world will open up. If not, then Republicans will sweep back in, and Democrats will be forced back again into a mode of supporting candidates and platforms that they really despise.