I once heard it said that U.S. political parties (Republicans and Democrats) have both spent the last century becoming increasingly liberal, such that 21st century Republicans now hold the same left-leaning or liberal outlook as Democrats once held in the mid 20th century. Similarly, the Democrats allegedly are more liberal now than ever before.
What sources or books should I study to validate or invalidate this idea, and study it further?
It seems that the most controversies between the political parties in the US lay outside of left-right dimension. In other countries these issues (LGBT, abortions, capital punishment, women rights, ban on smoking etc) would be considered non-political entirely because "political" usually means connected to left-right dispute. In Russia one can say "I decided to leave politics, I will struggle for gay rights now on" or "I decided to leave politics, I will fight for ban on abortions".
From this point of view, the US political parties seem to not to engage in politics at all.
I think the both political parties in the US ideologically identical, being both liberal (in international meaning rather than US meaning of the word).
Update. Recently, for example, there was a rally in Russia against a new copyright-protecting law that would allow to ban internet sites for copyright violation. The organizers of the rally stated in their announcement that "political banners are not allowed" and that the rally is "entirely non-political".
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.
The idea can't be validated, given that it rests on theoretical constructs that are fundamentally language based, and moreover empirical. It could potentially be invalidated.
Firstly you need a theoretical construct that defines "liberality" "illiberality" "left" and "right." The most common theoretical construct underlying the left-right divide is the issue of socialisation of the means of production, either under workers' control or through nationalisation within capitalism posed as a "left" condition; with the untrammelled conditions of the market (moderated by socially conservative institutions) posed as the "right." This spectrum has a two hundred year history, more or less, and is commonly understood with Roux and the Montagnards of France being the definitional case of "the left."
Other views are possible, consider perhaps the "Nolan chart" whose constructs are less firmly embedded in schematic political science, but whose conception of a scale of personal freedom amounting (largely) to personal liberality versus social conservatism may fit.
You would then need to assign parties to the scale over time. This could be done by looking at their intended policies, their implemented policies, or the actual social effects of their implemented policies—three very different things. I would suggest political, social and economic history here.
Finally you would need to compare the party movements to your posited example.
I would suspect from the classic "left-right" scale that both parties in the United States have been moving right, as they have both attacked social welfare institutions, supported the right of the market to dominate and exploit proletarians, union busted, wound back social programmes and are usually given as the definitional examples of neo-liberalism in practice. Correspondingly the time-linked access to share of the economy (ie: wages and social benefit income) of proletarians in the United States has shrunk since the 1960s compared to profit shares; and, those previous professionals who were paid extraordinary wages have become increasingly reduced to proletarian statuses. From this relatively common perspective both parties in the US have moved from centre-right to hard right, with the difference being made up based on their varying positions regarding the legal and economic position of women, ethnic groups, racial groups and glbti people.
The statement in the original question seems to come from a political conservative perspective. For more information, one might profitably consult the speeches of Ronald Reagan, who explicitly identified three elements of political conservatism: religious conservatives, national security conservatives, and economic/libertarian conservatives, and examine their concerns in more detail.
From this point of few, religious conservatives have been concerned with trends in government policy on abortion, a perceived anti-religious (more specifically, anti-Christian) secular bias in jurisprudence, and increasing influence of extreme feminists and homosexuals.
National security conservatives have been been concerned with military policy and international affairs, such as distrust of former and remaining Communist countries and virulent anti-American sentiment in the Islamic world.
Economic/Libertarian conservatives have been concerned chiefly with the size and scope of government (chiefly the federal), increasing government regulation generated from within federal bureaucracies, the growth of entitlement programs and transfer payments, uncontrolled deficit spending, and the practice of the judicial veto.
