By Daniel Indiviglio and Martin Hutchinson

The authors are Reuters Breakingviews columnists. The opinions expressed are their own.

Mitt Romney won the New Hampshire primary but Ron Paul’s showing could have as big an effect on the race. After finishing third in Iowa, the Texas Republican placed second in the Granite State, securing nearly one in four votes. That keeps him in the hunt to challenge Romney for now and could inspire him to make a third-party run later. Either way, the longer Paul sticks around, the more the national debate is likely to shift on important economic issues.

Paul’s crusade against the Federal Reserve will keep the spotlight on the central bank and Chairman Ben Bernanke. Paul’s desire to strengthen the dollar and sharply raise interest rates could resonate with voters, especially if inflation noticeably picks up by summer. And Romney and Barack Obama would be put in the unenviable position of supporting a weaker dollar, or explaining a more nuanced view on a complex subject.

The matter of domestic spending will stay front and center with Paul around, too. He would cut to the bone, while Romney and Obama are more inclined to slice surgically, if at all. The libertarian-leaning candidate would axe at least five agencies, including the Environmental Protection Agency, and push harder for expanding domestic oil exploration than Romney, potentially leaving him on the defensive.

On tax reform, Paul is also more aggressive than Romney. While the frontrunner would extend the Bush-era tax cuts and make other small tweaks to the code, Paul wants a bigger overhaul. His push for simplification, ending many deductions and a flat tax will keep the hot-button issues on the agenda.

The biggest distinction would be on foreign policy. Paul wants to hack military spending and engagement deeper than either Romney or Obama, perhaps even pulling U.S. troops out of Europe. He also wants less U.S. funding for the United Nations, World Bank and International Monetary Fund. That’ll leave the other two candidates trying to tell voters why their tax dollars should help defend far-flung nations or stabilize their economies.

A third-party run by Paul probably would ensure an Obama win. It would also, however, make the president answer uncomfortable questions and even catalyze some subtle but important shifts in policy.