When the left was most ascendant, the issues they rode to that success were economic in character. Think of the decades-long dominance of the New Deal coalition.
The premise of those economics were clear: one of the important roles of the central government is to counter-balance the power of big business and the rich - through things like:
1. Steeply progressive tax rates (the top marginal tax rate (the rate charged in the highest portion of rich folks' income) during even the administration of that notorious Leninist, Ike, was between 91 and 94 percent)
2. Support for Unions in the Wagner Act and other initiatives, to give bargaining power to labor, either directly (for union members) or indirectly (for other workers in unionized industries whose wages rose to match the union workers')
3. Public Works to take up slack in the labor market during recessions (the interstate highway system, the TVA, and much else.
4. Strong support for a minimum wage, to exert pressure "from the bottom" on wages further up the income scale
...and much, much else.
The Democratic Party would do well to build a new identity whose foundation is economic and strongly populist. There are too many people who call themselves "liberal" because they are pro-choice, eat organic food and drive a Prius - while opposing things like Single-Payer Healthcare, raising the minimum wage, ensuring a supply of affordable housing for everyone, the Employee Free Choice Act and much else. You know, the kinds of things New Dealers would do (and benefit electorally from.)
I sometimes wonder whether Harry Truman would even recognize the Democratic Party today.