Only in the economic and political senses. Socially and culturally, the country was far more conservative under FDR than it was under Ronald Reagan, much less Donald Trump. The leftism of that time was a completely different animal, however much today's lefties want to claim continuity.
What Communist country, or Left prior to the "new left," supported homosexuality or this "transgender" nonsense? The "western" Left has gone stark-raving mad on causes Karl Marx never imagined. Of course, the fact that Communist countries tend to be socially conservative doesn't bother the hippies any. Their goal is to stick it to the "rednecks," which they do by supporting Communist countries, Black Fundamentalists, islamic theocrats, and homosexuals simultaneously. As I've often remarked, today's Leftist coalition resembles nothing so much as the "heel" dressing room in the days of old-time, "kayfabe" professional wrestling.
Only in the economic and political senses
Economically, the US was much further Left (in the sense of the classical Left's concerns, rather than the modern Left's) in the 1970's than it is today. Richard Nixon, a Republican President, signed wage and price controls into law today. Not even Obama, and certainly not Bill Clinton, would have done the same in recent times. Both politicians were much friendlier towards state social welfare program expansion then than today (again, including Republicans such as Nixon - who signed a lot of alphabet agencies hated by conservatives into existence and supported a state-subsidized health insurance program that by today's standards is to the Left of Obamacare).
I think that what has happened is this: today's "New" Left has given up on trying to be the movement or party that claims to defend the interests of the working and lower middle classes from abuses of corporations and finance. Sure, you get some traditional anti-capitalist rhetoric from Bernie Sanders and the "occupy Wall Street" clowns, but these are Democrats who haven't got the memo yet. The ones who are in with the program are fully in bed with big business (especially Silicon Valley) and Wall Street. Wall Street firms now give more money to Democrats than to Republicans, and every almost big name in Silicon Valley (Jobs, Cook, Zuckerberg, Bezos) is a big donor to Democrat causes.
The New Left has a symbiotic association with Big Business: in return for Democrats supporting "free trade", open borders (cheap labor), and agreeing to go along with Republican tax cuts and de-regulation, business elites are happy to play along with the cult of racial/cultural diversity, LGBTQXYZ issues, and radical feminism. Doing so costs them nothing financially. Similarly, Democrats decided to write off the working class (at least the white working class) in favor of pandering to racial and sexual minorities, which doesn't require old-school Left class warfare rhetoric (only racial warfare rhetoric, directed against whites) or supporting policies that impede the interests of big business and big finance in any way.