^ I'd actually go with a Nixon victory in 1968, and the 1972 election proving that the Democrats have to move intelligently. Nixon doesn't resign and rides Watergate out and gets impeached as a result, Gerald Ford has to face a primary challenge from Ronald Reagan and as a result fails. Ted Kennedy never has the Chappaquiddick accident, and he beats Jimmy Carter in 1976 Democratic primaries and is elected. He serves two terms, passing a major health care reform act in 1978 among other achievements. His VP, Henry M. Jackson, proves to be a major supporter of national defense and does most of the foreign duties very well indeed, while Kennedy focuses on domestic issues.
Reagan wins the primary in 1980 but loses the election, which many in the GOP blame on the divisive influence of the "Moral Majority". Scoop Jackson dies of a heart attack in 1983 as in OTL. In the 1984 primaries, the surprise winner is the charismatic Governor of Arkansas, William Jefferson "Bill" Clinton. Clinton follows much of Kennedy's economic policies, which work very well in the 1980s. After their fourth-consecutive presidential loss in 1988, where George H.W. Bush and Orrin Hatch are beaten badly by Clinton, the Republicans switch out their hard conservative line and take a much milder tone in the late 1980s and early 1990s. Much-improved financial limits legislation comes in the aftermath of the massive Savings and Loan crisis, but the GOP, now having shed the "smaller government" line in favor of "government that works" and "efficient government", comes down hard on the Democrats, calling them too soft and complacent. Richard Lugar is the beneficiary of this and the Republicans defeat the Democrats in 1992. The plan by the GOP to run a moderate course is blown up by the hard-right, led by Newt Gringrich and Jesse Helms, who make a serious attempt to primary Lugar in 1996. This fails, but it ultimately costs Lugar re-election, allowing Lloyd Bentsen to rise to the Presidency in 1996. Bentsen, however, suffers a stroke in 1998 which harms his mobility and his health, and he resigns the Presidency on January 25, 1999, as a result of his illness. Vice-President Al Gore takes up the Presidency.
The GOP finally purges the last of the far-right in the aftermath of their loss in 1996. Gingrich oversees a massive, crushing loss in 1998 which sees the Democrats with a 62-38 majority in the Senate and 268-166 loss in the House and resigns as House Speaker in disgrace, though he had lost control of his party before then. The Democrats look to chart much more moderate positions, and the payoff comes quickly.
Gore struggles to hang on to a good position as President, and is soundly beaten by Arizona Senator John McCain in 2000, with McCain and Lincoln Chafee rising into the White House. Similar to the Kennedy/Jackson years, McCain spends most of his time on foreign policy issues and allows Chafee to run the domestic issues, a decision to which both men greatly benefit, and the pair are the first Republicans to be re-elected to the White House in 2004, soundly thumping Senator John Kerry and the scandal-plauged Senator John Edwards. The Republicans and Democrats still disagree on many things, but Chafee spends much of his time navigating waters between the two sides, and as a result the animosity that had been a hallmark of the 1980s-90s GOP disappears over time.
I'll get to the economics portions after I do a bit of research.