The Republican Party was conceived as the party of American industry. The Civil War era required the Republicans to take a stand against the expansion of slavery, since it was antithetical to the development of industry ("Free Labor, Free Soil"). During Reconstruction, the Republicans had trouble balancing the requirements of becoming a capitalist industrial power with providing opportunities for newly freed slaves. Providing opportunities meant expanding the role of the federal government but expanding the role of the federal government might interfere with the development of capitalist industry.

A perfect example of this conflict was southern sharecropping. The federal government experimented with land allocation programs to newly freed slaves but these programs didn't really take off due to the backlash of southerners who used the whole "inviolability of private property" defense, with which most Republicans were sympathetic. This resulted in ex-Confederates keeping most of their lands and hiring freed slaves as workers. As long as those workers entered into a voluntary contract with the land owner, that was good enough for northern Republicans. The fact that landowners enjoyed greater resources and knowledge than their ex-slaves made for an exploitative relationship in reality, but a perfectly acceptable one in a free market where people enter into voluntary agreements with each other.

This illustrates the fact that when capitalism clashed with civil rights in the GOP, capitalism usually won. Probably the single biggest political issue before the Progressive Era was the tariff, which Republicans generally favored since it protected American business and Democrats generally opposed since it raised prices and empowered northern business interests, which made up the bedrock of the Republican Party during the Gilded Age. The Democrats made some headway during this time, especially by adopting some Populist ideas, but the election of McKinley in 1896 marked a high point of sorts of American business influence in U.S. politics at the time.

This is around the time when TR started making a name for himself in the Republican Party as a reforming NY governor and an early hero of sorts to the emerging progressive movement. The GOP made him McKinley's running mate during his reelection bid in 1900 in hopes of garnering some progressive support and of neutralizing TR's political power by sticking him in the dead-end of the Vice Presidency. They did not count on McKinley being assassinated early in his second term, which let the TR genie out of the bottle and into the White House.

TR's presidency split the GOP b/t the progressives and business. Taft's presidency, which initially had TR's blessing, wasn't progressive enough for TR and his wing (things like the Ballinger-Pinchot affair hurt Taft's progressive bona fides) and this is why TR ran for a 3rd term by trying to steal the GOP nomination from Taft. TR's failure to do this marked a triumph of business interests over progressives in the GOP and led to the creation of a separate Progressive Party, which lasted well into the 1920s.

Meanwhile, the Democrats found their own reforming progressive governor in Woodrow Wilson, who won the presidency in 1912 thanks to the split in the GOP. Wilson was of course a flaming progressive in his own right and was able to bring in many progressive voters to add to the traditional Democrat base in the "solid south".

Then WWI can along and put the whole progressive movement on ice. The Red Scare after WWI made both parties weary of major reforms, so we get the business-friendly climate of the 1920s, presided over by 2 firmly McKinley-oriented Republicans (Harding and Coolidge) followed by a more McKinley-TR hybrid in Herbert Hoover. The market crash and the Great Depression sort of left the Republicans on the hook for everything, which went a long way in discrediting McKinley-style, laissez-faire government. The fact that Hoover tried some decidedly non-laissez-faire initiatives like the RFC and Hoover Dam hardly mattered. The GOP ideology of "the business of America is business" was discredited.

This opened the way for FDR, who had a similar story to TR and Wilson because he started as a reforming governor as well. He dusted off the Woodrow Wilson strategy of flaming reform (although he did not quite know what the "New Deal" he was promising would look like) while being careful to keep the solid south that was necessary for Democratic victory for the presidency.

The circumstances of the Depression and FDR's response to it made the Democratic Party the party of the working class. This is what historians generally mean when they refer to the "New Deal Coalition". It was a mix of northern workers and the solid south and would be the recipe for Democratic success up until 1964, when everything realigned.