The New Deal Coalition--liberals, urban workers, Southern whites, ethnic minorities--remade American politics.
Similarly, the late 1960's and 70's remade American politics. Civil rights brought racial minorities and white liberals more firmly into the Democrat camp, while it also set the stage for the Republican "Southern Strategy" in which alienated Dixiecrat Southerners shifted from being the Democratic Solid South for generations to, by the time of Newt Gringrich's 1994 Republican Revolution, being solidly Republican. "Movement" Conservativism beginning with Goldwater and culminating with Reagan was an attempt to bring ideological purity to the Republican Party, and one can see similar attempts by the New Left to bring ideological purity to the Democratic Party, especially around issues of the Vietnam War and minority (including women's) rights. This resulted in the present polarization of partisan identity, such that most Republicans are conservative and most Democrats are liberal, whereas before the 1970's you had liberal Rockefeller Republicans, mainly urban and Northern, and, mainly Southern, conservative Democrats. Issues like Evangelical Christianity, especially Falwell's Moral Majority, didn't really come into the mainstream until the late 1970's and early 1980's.
In the 1950's, there was a tremendous amount of political consensus. Famously, both parties sent out feelers to Eisenhower to see if he'd run on their ticket for president. Both parties were anti-Communist, the Republicans were just a bit more aggressively anti-Communist. The New Deal seemed like a mostly settled issue, and while there was still the anti-New Deal core of the "Old Right", someone like Eisenhower spoke firmly of creating a "progressive Republic Party" (I take that to mean pro-New Deal). The Republicans were more bro-business (Eisenhower got rid of the last Wartime price and wage controls) and the Democrats were a bit more pro-union, but no one was socialist by contemporary European standards and no one was strongly union busting.
I read on Ethel Merman's Wikipedia page that "Merman, a lifelong Republican, was a frequent guest at the Eisenhower White House." I'm just curious what made someone in that era lifelong Republican. Was it most likely the issues around Communism? Or was it related to economic policies? Kennedy's New Frontier and Johnson's Great Society of course sought to extend the New Deal. Adlai Stevenson, the Democratic nominee in 1952 and 1956, only carried the South (despite being a northern liberal "egghead"). Stevenson's ran on a very economic message and Eisenhower's main message seems to have been personal charisma ("I Like Ike"), with what Wikipedia tells me was a message emphasizing "Korea, Communism and corruption" layered on top of that. I get the sense that more Catholics, Jews, and ethnic Whites in general voted Democrat and so more WASPs supported Republicans, but non-WASPs were well represented in the incipient Conservative Movment (William F. Buckley and his brother-in-law L. Brent Bozell, the ghostwriter of Goldwater's Conscience of a Conservative, were both Catholics, and William Safire, may his memory be a blessing, was Jewish).
I'm just curious about what issues voters cared about in the 1950's and early 1960's, and what would lead them to pick one party so strongly over the other when they seem--at least to me--to be fairly similar. Were American politics really so focused on the degree of anti-communism and the relative belligerence of foreign policy, with a quiet consensus on domestic issues and an intraparty split on things like civil rights? Why do we see such a growing Republcian party in the 1940's and 1950's?
Keep in mind that partisan identity in this period had a stronger class basis than in more recent times (outside of the South, at least - where, with most Southern Republican voters effectively disenfranchised, the relevant divide was within the all-white and all-powerful Democratic Party).
The Democrats, as you have already observed, drew from a large pool of working class voters - skilled and unskilled, urban and rural, union and nonunion (though this group was definitely not as loyally Democratic as unionized workers were), workers in both the private and public sector, and poorer farmers. The Republicans, meanwhile, drew most of their support from business owners, professionals, managers, and white-collar workers, and they were most definitely the party of the upper class and the more affluent members of the middle class.
Additionally, there were stronger regional variations within both parties back then, with a lot of Southern Democrats being conservative (especially on race and labor issues) while a surprising number of Republicans in the Northeast, the more urbanized and diverse parts of the Midwest, and much of the West Coast (except for Southern California, which I'll come back to) holding moderate or even liberal/progressive views on different issues ranging from education to civil rights, from social welfare programs to whether America should take a more internationalist, pro-UN direction in foreign policy.
It should be noted that after losing five consecutive presidential elections (four to FDR, one to Truman) and winning control of Congress for only one term (only to lose control again to the Democrats), the Republican Party was on the defensive in the 1950s. This, IMHO, is a major reason for why Eisenhower was a comparatively moderate Republican President. People may have liked Ike, but they certainly did not like congressional Republicans; indeed, Eisenhower had very little in the way of coattails in either of his elections. Part of the major problem for the Republican Party at this time was that many regions (including many once proudly and loyally Republican regions - or at least, areas and districts within them - like New England, parts of New York and Pennsylvania, along with large Great Lakes states like Michigan, Illinois, and even Ohio (though to a lesser extent, granted) and much of the West Coast) were becoming more Democratic - in large part, because of changes in demographics. The previous Republican base of white, middle-to-upper-class (and, to a lesser extent, working-class) Northern Protestants and black voters was either becoming outnumbered (white Northern Protestants) or more worrisome, becoming much more Democratic (black voters) based on the ascendancy of the liberal, pro-civil rights wing of the New Deal Democratic coalition. For a little while during the post-WWII period, there were Republicans who enjoyed electoral and political success by running as moderates (or even, in some cases, as liberals) in areas that were either trending Democratic or were otherwise politically diverse and competitive. I am speaking, of course, of the so-called "Rockefeller" Republicans. But they never really managed to broaden the Republican Party's appeal in a way that really undercut the New Deal coalition; indeed, their strategy backfired on them, in large part because of the rise of movement conservatism and the New Right within the Republican Party.
Which brings me to your final question: Why did the Republican Party grow so much in the 1940s and 1950s? To answer this question, it must be noted that in the years immediately after the end of WWII, the ideological priorities, economic situation, and geographical distribution of the American electorate changed, with anti-Communism in the context of the Cold War becoming paramount in importance, with Americans of all classes (but especially working and middle-class white Americans) enjoying the greatest growth in and degree of economic prosperity ever in American history , and with the related moving of white, working and middle-class Americans to the rapidly growing mass suburbs (as opposed to the elite suburbs of an earlier era). Some of the most rapid degree in suburban growth was in the so-called "Sun Belt" of the South and the West: more significantly, much of this growth was directly related to the emerging Cold-War era military-industrial complex that Eisenhower warned about in his farewell address as President - and, in the local context in the Sun Belt region of extreme anti-Communism (which became anti-liberalism within the context of American politics), social and religious conservatism, virulent opposition to new civil rights legislation, and a gut hostility to unions on the part of the Southern/Sun Belt's overall political culture, it isn't hard to see why the South and the broader Sun Belt became THE flashpoint for the "new" conservatism, and the new base of the Republican Party. This was, after all, a region that had to be integrated into the Republican Party base, for the GOP had been on the decline in much of the country outside of the South and the Sun Belt. Thus, Rockefeller Republicanism was doomed by the GOP's demographic shift to the South and West along with the fact that in most areas, it was an elite minority position within the party - hardly a recipe for intraparty popularity, much less electoral success!
This is a long answer, but I tried to shed some light on this period in American politics to the best of my ability.
Some helpful sources:
McGirr, Lisa. Suburban warriors: The origins of the new American right. (2001)
Phillips, Kevin P. The emerging Republican majority. (1969)
Those at /r/politicaldiscussion may have some insight as well
