The Answer: Yes and No
The basics of our mixed market-economy --- which generally has had much less statist regulation, lower taxes, and lower redistribution of income by means of governmental policies, a similarity shared by Britain, Australia, New Zealand, Ireland, and to an extent Canada: in short, the major English-speaking rich countries --- will undoubtedly remain intact as we emerge from the current crisis.
There will still be a largely private enterprise system, more entrepreneurial dynamism than found in other industrial countries --- an observation pinned down by numerous cross-country survey-data, an unusually high-quality R&D base, and as a match to all these national economic endowments, a vigorous pace of innovation across the entire economy itself. That said, there will also be far more energetic and watchful regulation of financial sectors, a likely reduction in defense spending as governmental expenditures shift more toward a larger government role in health care --- with, we hope, a gradual reduction in current health spending as a percentage of GDP (around 15%, about 40-50% higher than in other industrial countries) --- somewhat higher taxes on the very affluent and rich . . . and so, as you add it up, an overall larger role for the public sector.
Beyond that, who knows?
We have very flexible institutions in both the public and private sphere . . . not to mention a population that is unusual among advanced rich countries for its adaptability and acceptance of change. Innovation of all sorts will be booming with high-octane vigor over the next decade . . . just as it did in the era of the Great Depression of the 1930s, during WWII, and repeatedly since 1945. In effect, as recent scholarly work has shown, so far the USA is the only country to have fully exploited the productivity-enhancements inherent in the Internet age.
Enter Today's Commentaries on This Subject
At two different economic web-sites --- one run by Professor Mark Thoma (a New Keynesian) and the other by Professor Tyler Cowen (a flexible and moderate libertarian) --- prof bug engaged their initial posts, then other professors in his lengthy replies. The general thrust of these replies? The buggy stress on the role of institutions in handling effectively or not major disruptive shocks to different national economies across the world. Oddly, it's a subject ignored by probably 95% of well-known economists. These days, you see, the big rewards in economics come to the use of formal and abstract statistical models, which have trouble coping with the realities of concrete institutional frameworks for each society.
No need to say more.
Start here for the initial buggy commentary, found at Professor Thoma's Economist's View. Be sure to run a find --- "buggy" --- for some replies. Then go to the Marginal Revolution and click here for prof bug's lengthy 2nd comment . . . followed on the next page by a brief one and a reply by others to that 2nd comment.