Arnold Kling asks this question, so I thought I'd try a stab at it, but trying to cast progressivism in the best possible light. Of course my answer is not exclusive to Arnold's, as we might both be right about the elephant. From an outsider's perspective, here is my take on what progressives believe or perhaps should believe:
1. There exists a better way and that is shown by the very successful polities of northwestern Europe and near-Europe. We know that way can work, even if it is sometimes hard to implement.
2. Progressive policies offer more scope for individualism and some kinds of freedom. Greater security gives people a greater chance to develop themselves as individuals in important spheres of life, not just money-making and risk protection and winning relative status games.
3. Determinism holds and tales of capitalist meritocracy are an illusion, to be kept only insofar as they are useful.
4. The needs of the neediest ought to be our top priority, as variations in the well-being of other individuals are usually small by comparison, at least in the United States.
5. U.S. policy is not generally controlled by egalitarian interests, So it is doing "God's work" to push for such an egalitarian emphasis at the margin. At the very least it will improve the quality of discourse, even if the U.S. never actually arrives in "progressive-land."
6. Limiting inequality will do more to check bad governance than will the quixotic libertarian attempt to limit the size of government.
7. Skepticism about the public sector is by no means altogether unwarranted, yet true redistributive programs are possible and they can work and be politically popular; we even have some here in the United States.
8. We should support free trade, more immigration, and more foreign aid, but the nation-state will remain the fundamental locus for redistribution. That means helping the poor at home more than abroad; a decision to do otherwise would destroy political equilibrium and make everyone worse off.
9. State and local governments are fundamentally to be mistrusted (recall segregation) and thus we should transfer more power to the federal government, which tends to be bluntly and grossly egalitarian, when it manages to be egalitarian at all. That is OK.
10. The United States has to struggle mightily to meet the progressive standards of western Europe and we should not equate the two regions in terms of their operation or capabilities. Yet there is an alternative strand in American history, if not always a dominant one, showing that progressive change is possible. Think Upton Sinclair and Martin Luther King and the organizers of early labor unions.
11. The evidence on economic growth is murky and so it is not clear that doing any of this carries much of a penalty in terms of future growth. In some regards it will enhance the especially beneficial sides of economic growth, even if it does not boost growth overall.
In due time I'll be writing more systematically about why those views are not, on the whole, my own. But not today!
It would be interesting to see a progressive try to sum up an intelligent version of libertarianism.