This coalition has many parts. It is based on the idea that the majority of Americans are, at heart, relatively conservative both economically and socially.
On the social side, this coalition was based on the "religious right." These were evangelical Christians. They were also joined by conservative Catholics and by Mormons.
On the economic side, the coalition was based both on "Reagan Democrats" and on wealthier people. The Reagan Democrats were largely blue collar workers who disliked taxes while the wealthier people were more of "true believers" in the Republican ideas of laissez-faire capitalism.
The coalition, then, was a coalition of blue collar white workers (particularly men) along with conservative Christians and wealthier people.
The Republican coalition that led to this dominance was made up of traditional Republican constituencies and of "Reagan Democrats."
The traditional Republican constituencies were mainly well-off people who believed in economic conservatism. The Republicans were seen as the party of the rich. They were also the party that was most "hawkish" in terms of foreign policy. Republicans came to dominate, however, as they picked up "Reagan Democrats." These were largely middle class and blue collar whites. Many of them were in the South and the Midwest. These voters gravitated to the Republican Party because of its opposition to things like welfare and its support for traditional social values.
The political era that you describe, which Princeton historian Sean Wilentz has characterized as "the Age of Reagan," began to take shape in the late 1970s.
According to the historians Thomas Byrne Edsall and Mary D. Edsall, liberals gained an advantage during Watergate, but it would not last. Steadfast Republicans were also scandalized by the breach in civil liberties committed by the Nixon Administration. This outrage led them to vote for Jimmy Carter in 1976. However, this national shift to the left was uniquely related to the circumstances of the time; it was not an ideological shift. Those conservatives returned to the Republican Party when Ronald Reagan, former governor of California, ran for office in 1980.
Reagan's ability to entice white, male, blue-collar voters, as the previous educator mentioned, could be due to two factors: his ability to create a strong masculine image during an era in which women and gays were making strong gains in civil rights, and his promise to cut taxes. The latter factor may have been more important.
According to the Edsalls, family income stopped growing after 1973, but the tax burden increased due to inflation. An increase in unemployment rates led to an expansion in welfare programs, which were funded by these tax dollars. It is no secret that people of color are more heavily impacted by economic recessions and, therefore, more likely -- in proportion to their respective population -- to rely on welfare programs. White working-class voters did not usually recognize this complex intersection of race and class and tended only to see that their hard-earned dollars were going to people unlike themselves, people whom they may have believed were less deserving of assistance.
To complicate matters around race and the decline of white supremacy, black politicians began to make political gains, particularly those who became mayors of major cities. Affirmative action programs also expanded; and busing, which began in the early 1970s and continued into the mid-seventies, became a much contested method of school integration. Also, liberalized immigration policy led to a surge in non-European immigration and an expansion of public services to recent arrivals. This, in turn, created competition for employment, particularly in sectors previously dominated by the white working-class.
The white working-class's ambivalence toward the Democratic Party caused later politicians, particularly Bill Clinton, to make their ideas more centrist.