That’s Hillary Clinton, right? Yes, but Republican Mike Huckabee also routinely tells this podiatry story to make the exact same point. John Edwards, Barack Obama and the other Democratic candidates are also talking about the backward economics of the health-care industry. Check back in a couple of years and it’s a good bet more insurance companies will be reimbursing your local foot doctor for treating diabetics, and the number of amputations may even decrease. That will be a sign that a major transformation of the health-care system toward prevention is underway, courtesy of our much-maligned presidential campaigns.

It is the Law of Unintended Campaign Consequences. Amid the endless polls, attack ads and silly flaps, a strange dynamic is at work. Secondary issues—often stump-speech afterthoughts—can work their way into the political bloodstream and yield larger results than the issues that seem to be the major concerns of the day. The originators of these ideas don’t always win the election, but they leave us something important to remember them by.

There’s a long history of seemingly minor statements from the campaign trail resonating far beyond Election Day. During the 1960 Democratic primaries, Minnesota Sen. Hubert Humphrey talked about a bill he had proposed that was going nowhere. The idea was to send idealistic young Americans overseas to help in the developing world. Humphrey lost the nomination to John F. Kennedy, who featured Humphrey’s notion in a speech that he gave at the University of Michigan. After JFK became president, the idea reached fruition as the Peace Corps.

In 1976 former Georgia governor Jimmy Carter was the first to use the Iowa caucuses as a springboard to the White House. His message was “a government as good as its people,” and buried in his remarks was a vague reference to matching progress on domestic civil rights with a new emphasis on human rights abroad. After he won, this became the cornerstone of his foreign policy and, three decades later, human rights remains central to today’s debate.

When Bill Clinton was roaming New Hampshire in 1992, trying to distract himself from his troubles with Gennifer Flowers and his draft record, he often waded deep into policyspeak. His aides rolled their eyes when he mentioned something called the “earned income tax credit,” a minor Reagan-era program to help the working poor keep a little more of their wages from the IRS. But by the time President Clinton’s term ended, the EITC was one of the most powerful anti-poverty programs in American history, lifting millions into the middle class.

In 2000, millionaire publisher Steve Forbes ran for president. Forbes was a weak GOP candidate, but he started getting traction in the polls with his flat-tax proposal. George W. Bush felt obliged to match it, though the Texas governor himself had little interest in tax cuts for the very wealthy. The result was the plan for steep tax cuts for upper-income Americans enacted in 2001. Sometimes it seems everything in politics is connected to everything else. Seven years later, every Democratic candidate now wants to repeal those same Bush tax cuts and use the money to finance health-care proposals. We take this for granted now, but the center of gravity shifted on raising taxes when hardly anyone was looking.

Education is another area ripe for sleeper issues. In early 2007, when he was an asterisk in the polls, Huckabee distinguished himself from the rest of the Republican field in part by discussing the importance of art and music education in the schools. He explained how right-brain development is important not just to enrich the lives of students but to inspire the creativity necessary to help the United States keep its edge in the global economy.

At about the same time, New Mexico Gov. Bill Richardson sounded the same note in his stump speech as part of his call to end No Child Left Behind. Huckabee’s surge has little or nothing to do with this fresh idea, and it won’t resurrect Richardson’s campaign. But both Clinton and Obama now mention the subject by way of explaining why they think No Child has tilted too far in the direction of testing. It’s a strong applause line. Don’t be surprised if a lot more money for art and music turns up in an education bill a couple of years from now.

The lesson is that some of what’s said in presidential politics really matters, even if the candidate saying it doesn’t win. So the next time you see a contender bloviating on TV about some minor thing, stop and listen. That little proposal he’s mentioning might be pilfered by another candidate, one who winds up in the White House. Then watch what happens when the throwaway line you heard months or years earlier leaves a footprint so deep, even a podiatrist would be impressed.