Republicans and Democrats resemble one another too closely for voter comfort these days. Whatever their own political leanings, voters would prefer more diversity in the policy spectrum.

Consider the question of whether the federal government should increase spending. Politicians’ answers come in a broad range: “yes” or “yes, a lot.” Even candidates who talk about cuts are really only speaking about reductions in increases. In fact, politicians don’t believe they really can make cuts. No modern president has, or at least no president who took office in peacetime.

Not Bill Clinton, who told the nation the welfare era was over. Not even Ronald Reagan, the great free-market president of the postwar era. Budget cutters, the assumption runs, can’t get elected. Federal austerity, the politicians often warn, might hurt the economy anyhow. Presidents just can’t say “no.”

But there have been peacetime presidents who said “no.” Two were presidents we scarcely hear about anymore, Warren Harding and Calvin Coolidge. The 29th president died amid scandal in 1923 — but not before cutting the federal budget. Coolidge then served 5 1⁄ 2 years, to 1929, a period when the population and the economy grew. Yet when Coolidge left the White House and returned to his hometown of Northampton, Mass., the federal budget was actually lower than when he came in.

How Harding and Coolidge managed to say “no” is a good story and one that couldn’t have happened without the contribution of the nation’s greatest banker, Andrew Mellon.

The story starts in 1920 and in a fiscal landscape that would seem familiar. As today, the federal debt loomed over the future. Yet tax rates, ranging into the 70s, could hardly be pushed higher. The government had expanded, but various groups were pressing for greater federal spending. World War I veterans did not all find jobs and many were disabled — they sought a pension or a bonus.

With commodity prices bouncing up and down, farmers demanded some kind of subsidy stream as well. The presidents lacked control or even oversight of the budget: Congress called the shots. Yet Harding, an ebullient senator of Ohio, and Coolidge, a quiet governor of Massachusetts, ran and won on a ticket of “no.” They would say “no” to both high taxes and government expansion.

Harding did some of the first hard work of cutting. He shepherded through the Budget and Accounting Act of 1921, which unified the budget process under the president and gave the White House the power to impound and sequester. Harding also cut the budget and vetoed veteran pensions and farm subsidies.

Harding appointed Mellon as Treasury secretary, and Mellon adroitly rescheduled the debt; Harding and Mellon also passed a round of tax cuts. Harding was not a “naysayer” by temperament. He disliked using the veto on his old Senate colleagues. He appointed friends, rather than professionals, to key posts. Their corruption tainted his reforms and aborted them.

Few reckoned that Coolidge could continue or complete what Harding had started. Voters figured Coolidge was a lame duck, “the accident of an accident.” The real Republican candidate would emerge in 1924. Coolidge’s colleagues in Washington didn’t expect much either: “Coolidge had little about him that was regal,” recalled George Wharton Pepper, a senator of Pennsylvania.

Still, Coolidge pushed forward where Harding had hesitated. He and Mellon sought and received several more rounds of tax cuts, bringing the top marginal income tax rate down to 25 percent, a level even lower than Reagan’s. In his years observing railroads, Mellon had noted that when you cut the toll for a rail line, you might get more business. An owner charged, as Mellon put it, “what the traffic will bear.”

Mellon thought the same principle might apply to tax rates. Perhaps lower rates would permit more business activity and therefore bring higher revenues. Today we call this philosophy “supply-side economics.”

Coolidge was not as enthusiastic. His thrifty temperament led him to obsess about the budget. In fact, the president kept twin lion cubs, which the White House named “Tax Reduction” and “Budget Bureau.” The point was that the lions were twins: Fed on steak, they weighed the same. To match Mellon’s tax cuts, Coolidge kept up with budgets. He also vowed to prevent future spending. “It is much more important to kill bad bills than to pass good ones,” Coolidge had written his father years before. As president, Coolidge “killed” 60 laws by veto, compared with Harding’s record of six.

The result of Mellon’s partnership with Harding and Coolidge pleased most Americans. Government became smaller; the number of strikes fell. Mellon had won his bet: Revenues for the government actually increased from 1924, even though tax rates were lower. The team lowered the debt by a third. Working-class families became middle-class when they found they were able to acquire new comforts such as Model Ts and Model As, electricity, and indoor plumbing. The 1920s were not the fragile illusion depicted in, say, “The Great Gatsby.” Voters knew it and rewarded the pro-austerity Coolidge in 1924 with a resounding victory.

Under Herbert Hoover, policy shifted, with the White House becoming active. This shift, indeed the whole story, is little known, in part because people blame the Great Depression of the 1930s on the 1920s. But that is misplaced. As I noted in “The Forgotten Man: A New History of the Great Depression,” the economic crash had multiple causes. Few had much to do with policies from 1920 to 1928.

Knowing about the Harding-Coolidge-Mellon record doesn’t assure us that voters will elect to the White House a candidate who says “no.” Knowledge of that forgotten record merely broadens the range of options politicians can feel comfortable offering to voters today. That is, such knowledge makes a candidate who says “no” possible. And asked whether a wider range of policy choices represents an improvement, even those who oppose such policies will probably want to answer “yes.”