This is more or less my belief - that said, I don't think even Obama would be able to win 4 elections in a row. We're reaaaaaaaally fickle, and it's only gotten kinda more swingy with the polarization.
If the GOP nominates someone sane (Paul Ryan would be my best bet, with Haley as a VP pick); then I think they'd be at 60/40 to win the election barring anything extremely unusual happening during the next four years (massive economic boom, for instance). I think the economic decline is here to stay, and I think the Democrats are going to be stuck with being blamed for that.
Oddly enough, parties seeking either a fourth consecutive presidential election victory or a fourth consecutive term (more on that distinction later) have a 4-3 record.
Successes
1) James Madison won a fourth term for the old Republicans (or "Democratic-Republicans") in 1812. They would go on to win seven straight, although the sixth was virtually uncontested and the seventh was fought among factions within the party. The party broke up in the aftermath, with the different factions eventually coalescing into the Democratic Party and the Whig Party.
2) William Howard Taft won a fourth term for the Republicans in 1908. This was also followed by a party split as Taft's own predecessor, Teddy Roosevelt, ran a third party challenge under the banner of the Progressive ("Bull Moose") Party in 1912 after unsuccessfully challenging Taft for the Republican nomination. This resulted in Woodrow Wilson earning an Electoral College landslide for the Democrats with only 42% of the popular vote (Taft came in third in both the electoral and popular vote). The split proved short lived as most Progressives, including Roosevelt, returned to the Republican fold in 1916.
3) Franklin Roosevelt won a fourth consecutive term for both himself and the Democratic Party in 1944. Harry Truman would capture a fifth term for the Democrats in 1948 before the Republicans won back the White House behind Dwight Eisenhower in 1952.
4) Now here's where the distinction between four consecutive victories and four consecutive terms comes into play. The Republicans won six straight presidential elections beginning in 1860, but since Abraham Lincoln ran with Democrat Andrew Johnson in a unity ticket in 1864 and Johnson assumed the presidency after Lincoln's assassination, there was a Democratic administration in there. If your standard is four straight victories, then you count Ulysses S. Grant's victory in 1872. If your standard is four straight terms, then it's James Garfield's victory in 1880. Either way, you get one success.
Failures
1) Democrat Martin Van Buren (namesake of the
infamous street gang) was defeated for re-election in 1840 by William Henry Harrison of the Whig Party.. Van Buren was blamed for the
Panic of 1837 and subsequent depression by much of the electorate. Harrison is probably best known for having
the shortest presidency in US history. Van Buren resurfaced as the nominee of the Free Soil Party in 1848, finishing a distant third.
2) Republican Herbert Hoover lost his bid for re-election to Franklin Roosevelt in a landslide in 1932 as voters blamed him for the Great Depression. There's really not much else to say about this one, although Hoover did rehabilitate his personal image, though not his presidency, somewhat during his long post presidency.
3) Republican George H.W. Bush was defeated in his 1992 bid for re-election by Bill Clinton. Popular myth attributes his defeat to the strong independent candidacy of Ross Perot, but
exit polls actually suggest Perot drew equally from Bush and Clinton. A far more significant factor was the high unemployment that resulted from the early 1990s recession.
I don't think this really tells us much about 2020. For starters, seven is not very many data points. Also, most of these elections were fought under circumstances that clearly favored one party over the other. The opposition Federalist Party did OK in 1812, but they were in the middle of a slow death. Post Civil War the Democrats were at a disadvantage as Northern voters tended to blame them for the War. FDR was a popular wartime incumbent in 1944 and Democrats were still tying the Republicans to Hoover's unpopular presidency. But I must admit I was a bit surprised when I went through the results and found this.