I could see him gaining strong approval ratings for promising to scale down and end the Viet Nam war, but then suffer a bit when it takes longer than he had hoped to do so. He would still have strong support from the liberal base, including the youth, most Dems and some of the more liberal Reps.
Come '72 he would still have a slim chance of beating Ford or Dole. But a younger Reagan would probably clinch the nomination and give Humphrey a real run for his money, attacking him on his sluggish winding down of Viet Nam and tapping into the nation's Democratic fatigue (at this point they had won every election since 1932 except '52 and '56 – that's 8/10). Being the "change" candidate, Reagan/Dole would defeat Humphrey/Muskie by a narrow PV margin but a comfortable one in the EC, probably garnering in excess of 350 EVs.
We get the energy crisis and recession early in Reagan's term, which initially puts his approval in the lower 50s. But the situation seems to be improving (superficially) by late '75, and during his re-election campaign the administration spins the economy numbers to mask the reality – stagflation, which IRL Carter got blamed for. Reagan is charismatic, funny and looks good on the economy. The Dems realize the election is theirs to lose, so most of the better candidates bide their time until 1980. There is no Carter because there is no Watergate and no Ford, so they eventually nominate Jerry Brown. Reagan easily defeats him, with a PV margin of 4-5m and in the low 400s in the EC.
However, with the Soviet Union still rising in power, a greater proportion of moderates and liberals in the GOP, and a split congress (I'm guessing R Senate and D House), Reagan's conservatism is not as extreme and he does not become such a legendary figure within the GOP.
The Republican primary in '80 is between Dole, HW Bush, John B. Anderson and Pat Robertson. The race narrows down to Dole and Anderson, but Dole manages to trump up his experience and soon racks up a large delegate lead. Anderson predictably drops out and continues to run as an independent. meanwhile, the Democratic primary consists of Ted Kennedy, Walter Mondale, Lloyd Bentsen, Sargent Shriver and Scoop Jackson. Jerry Brown declines to run again. Kennedy is of course the heavy frontrunner throughout, and though some minor candidates get "favorite son" bumps in their respective home states, Kennedy proves unstoppable and easily wins the nomination.
Reagan's second term was marred by stagflation, unemployment, and the ever-growing Soviet threat, which Reagan was not able to deal with as effectively as IRL. Although there is no hostage crisis, the GOP's credibility is damaged and Kennedy shows a small lead in the polls throughout election season, and he destroys Dole in the debates. Dole struggles with his image, and distances himself from Reagan due to the poor economy. Anderson is largely overlooked, and draws a few votes from both major parties, but not enough to sway the election in either direction. Kennedy/Bentsen soundly defeat Dole/Bush by an EC margin of nearly 300 EVs and a PV margin of about 5m. Anderson receives just over 2m votes and no EVs.
This is my first attempt at putting an alt history in writing, so if anyone is interested feel free to give feedback/criticisms/suggestions, or keep going with it!

Also, I would post maps but I don't have enough forum posts yet.