About Coolidge: His problem is, he's a mundane president even if the Conservatives love him, because he didn't do anything. That was essentially his Presidency; to make the President as much of a non-entity as possible. Because Coolidge was a mundane, boring man. He was Adlai from Futurama.
That's the thing: the Coolidge love is largely based on a philosophical belief about the proper role of political leaders, that under most circumstances, high Presidential activity levels are a vice, not a virtue. Coolidge actually did accomplish a fair amount, but he's remembered for being staid, quiet, even-tempered, and modest, and thus attracts a fair amount of admiration for his attitude among those who prefer that style of political leadership.
I'll confess to being a bit of a Coolidge fan myself, and I've heard a fair amount of admiration for both Coolidge and Harding from among my fellow small-l libertarians and similarly from many fiscal conservatives.
The case for Harding is that he rolled back a lot of Wilson's bad (from a conservative or libertarian perspective) policies, especially in terms of cutting both taxes and spending. His admirers credit his administration's policies with quickly ending the depression of 1920 and setting the stage for the sustained economic boom of 1921-1929, and note that his policies (despite massive tax cuts) reversed the deficit he'd inherited from Wilson and (over the course of the subsequent Coolidge administration) paid off over a third of the national debt.
The case for Coolidge over Harding (in addition to the stylistic admiration of his "Silent Cal" image) is that Coolidge shares most of the credit for the accomplishments attributed to Harding by Harding's admirers, but without much of Harding's baggage. Harding's memory is marred by a major corruption scandal where Harding's Secretary of the Interior was caught taking bribes. Harding's role in this Teapot Dome scandal is somewhat overstated in the prevailing historical view, I think, in part because the scandal broke shortly after Harding's death (making him a convenient person for other people tarred by association with the offenders to shift blame to), but he does deserve a certain measure of blame. While Harding wasn't personally implicated, Harding was in charge and was ultimately responsible for policing his cabinet, which he didn't (Harding appears to have been completely oblivious, and the scandal was broken by a Senate investigation), and Harding also gets a measure of blame for being the one who appointed the corrupt Secretary Fell in the first place, in addition to the blame for failing to supervise him properly.
Coolidge continued the policies that Harding's admirers credit him for (especially tax reform: the top income tax rate was 73% when Harding took office, 50% when Harding died and Coolidge became President, and 25% when Coolidge left office), and most of the positive effects credited to Harding's economic policies (the 20s boom and the paying down of the national debt from $26 billion to $16 billion) took place mainly under Coolidge. But Coolidge's hands were completely clean of Teapot Dome, so an admirer of the joint Harding/Coolidge economic policies can safely admire Coolidge for continuing and extending them without accepting the taint of Harding's association with Teapot Dome.
There's all sorts of theories about blame for the Great Depression, but it's worth noting that several of the major theories place at least some blame on both Harding and Coolidge:
- Milton Friedman's "Great Contraction" theory holds that the Great Depression would have been a relatively minor recession but for active mismanagement by the Federal Reserve and the Treasury, which made the wave of bank failures and personal and business bankruptcies far worse than it should have been, by refusing to carry out the Fed's statutory duty to bail out illiquid-but-solvent banks (i.e. those which have sufficient assets to pay their bills, but due to a bank run or other difficulty need a short-term bridge loan to avoid bankruptcy), and by making monetary and bank-regulation changes that pulled a huge amount of money out of circulation (causing a deflationary death spiral, as the reduction in the money supply cut prices and wages and left lots of people, banks, and businesses unable to pay their debts and other contractual obligations). Under this theory, two of the major villains were Treasury Secretary Andrew Mellon (appointed by Harding and retained by Coolidge and Hoover, and the primary architect of the Harding/Coolidge fiscal policies) and Fed Chairman Roy Young (appointed by Coolidge).
- The Austrian School theory is that the 1921-1929 boom was largely illusionary prosperity due to a speculative bubble fuelled by loose monetary policy under the Harding and Coolidge administrations, and the stock market crash and waves of bank failures that triggered the Great Depression were an inevitable "hangover" from those policies as the bubble burst and everyone had to unwind the consequences of nearly a decade of bad investment decisions made under the false assumption that the asset bubble was a genuine boom.
- Nobody really thinks much of Hoover's role in the Depression. Nearly all economists think Hoover's tariff policy made things much worse, and there's likewise broad-based disdain for Hoover's support for wage and price fixing. Austrian-schoolers, Friedmanites, and Supply-Siders all agree that Hoover's decision to reverse the Harding/Coolidge tax cuts (raising the income tax back from 24% back up to the 70+% range) made things worse, and even many Keynesians support this view as well (raising taxes in a recession is generally considered contraindicated by Keynesians). Keynesians also fault Hoover for failing to do enough on the spending side to relieve the Depression (he did more than he's generally credited for, but significantly less than FDR did later, and most Keynsian observers feel even FDR did too little in terms of spending-based fiscal stimulus until WW2 broke out). Hoover's taint spreads to Harding and Coolidge by association, as Harding appointed Hoover as Secretary of Commerce, and Coolidge kept Hoover on in that role, and it was from his stature that role that Hoover was able to secure nomination and election in 1928.