I personally think it's going to be tougher to make the Republicans economic liberals that it will be to make the Democrats economic conservatives. While the Republicans had a relatively strong progressive wing, they were nowhere near as numerous within the GOP to the degree that Southern conservatives were within the Democratic Party.
Also, you have to take into account that 'conservatism' and 'liberalism' as they stood have very different meanings in both parties. Conservative Democrats were racial conservatives, while by-and-large, conservative Republicans, prior to the migration of the Dixiecrats into the party, were racial liberals. In that same vein, Republican 'liberals' were less likely to favor unions and generally more corporatist than Democratic liberals, who tended to favor unionism in toto because of the influence of the populist movement.
I think your best shot for this is a POD in 1948. Let's say that Hubert Humphrey's amendment to the Democratic platform to emphasize Civil Rights goes down. Thurmond's Dixiecrats stay in the party fold, but as a result, let's say butterflies turn African-American votes to Dewey, giving him the White House in 1948.
Dewey's Presidency is pretty much an earlier Eisenhower Presidency, complete with Brown v. Board or some equivalent. Dewey, along with northern Democrats and liberal Republicans push for civil rights, while the South solidifies further behind it's own 'Southern Manifesto'.
In 1956, the Democrats take back control of the White House with President Adlai Stevenson, who himself stays ambivalent on civil rights to avoid inflaming southern Democrats. Two terms of Stevenson further the boiling over point, while southern Democrats become even more powerful in the party structure. John Kennedy is nominated for President in 1964, though he will go down in defeat to liberal Nelson Rockefeller for the Presidency in this year.
Rockefeller pushes civil rights as Dewey did, inflaming the nation, especially the South. Southern Democrats and Conservative Republicans begin blurring, as the latter switch parties. Likewise, Northern Democrats slowly begin to join the Party of Lincoln, as have African-Americans en masse, ending a small blip in favor of the Roosevelt-Truman-Stevenson programs of the welfare state.
In 1968, Democrats nominate George Wallace for the White House, who himself will go down in defeat to a triumphant Rockefeller, though in a decidedly close election--closer than Rockefeller will have wished. His second term is plagued by stagflation and a rowdy American left, protesting against environmental degradation and in favor of women's liberation.
By the time Rockefeller leaves the White House in 1973, the parties are decidedly different in nature and scope. George Wallace is the de facto leader of the Democratic Party, despite being paralyzed as a result of an assassination attempt while on the campaign trail in 1972, and actor Ronald Reagan is Wallace's designated, electable-outside-of-the-south successor.
The Republican Party, under the leadership of President George Romney, has like-wised moved leftward on economic policy in response to it's growing African-American and minority base.