That's interesting. The argument I tend to hear these days is that the most liberal mainstream Democrat today is actually further to the right than Richard Nixon was. The argument there is that for the last 30 years Republicans have been championing views to the right of center, and Democrats have been trying to move to the center. This creates a new center further to the right, and then process repeats.
Who is right? I don't think you can really answer that, without having some kind of coherent theory of Politics and political "left" and "right". We don't really have that, but there are several competing theories out there.
Personally, I think it may be a bit of both. Cultures change, and values change. Political ideologies have to change too, or they will die. For example, almost nobody is seriously arguing for slavery or anti-miscegenation laws any more. In that way, the entire USA is way farther to the "left" that all but the most extremist wackos in the 18th and 19th centuries.
However, it is also true that very few people today are in support of socializing industries (like FDR did) or serious government effort to eradicate poverty (like LBJ), banning handguns, completely socializing the medical system, outright banning of the Death Penalty, etc. All of those used to be popular liberal causes. Good luck finding a politican running on any of those today in all but the safest liberal seats.
The Death Penalty is an intersting issue to study, as we have good polling data on it going back almost a century:
Note that there was a breif time in the late 1960's when more people were against it than for it. 30 years later, people were in favor of it 4 to one. Today, as in 1939, its more like two to one. So you could say, on this issue at least, we are exactly as "liberal" as we were duing the Depression.
So I guess my answer is the old Facebook cop-out: It's complicated.