The biggest winners of Tuesday’s Iowa caucuses may well be the guy who finished third and those pragmatic members of the Republican Party looking for a strong candidate to challenge the politically shallow Donald Trump and the extremely conservative Texas Sen. Ted Cruz.

Yes, Sen. Cruz won a clear victory, albeit with only 28 percent of the vote. However, it was the 23 percent showing for the third-place finisher, Sen. Marco Rubio of Florida, which may turn out to be the biggest story of the night.

If Sen. Rubio can capitalize on his momentum coming out of Iowa with a strong showing in the New Hampshire primary, he will strengthen his claim as the best candidate to unite the hard-right and moderate wings of the Republican Party. He has the ability to attract the unaffiliated and Democratic votes necessary to win the presidency.

With strong showings in New Hampshire, New Jersey Gov. Chris Christie or Ohio Gov. John Kasich could again muddle the fight to be the alternative candidate to Trump and Cruz. But at the very least, Sen. Rubio’s 23 percent third-place finish in Iowa has given hope to so-called establish Republicans that a viable alternative will emerge.

Though he has bounce back potential in New Hampshire, where polls have shown him well ahead, it was a bad night in Iowa for Mr. Trump. The billionaire real estate mogul made a tactical mistake in going for the brass ring in the farm state. In doing so he raised expectations, then failed to meet them, barely finishing ahead of Sen. Rubio. That hissing sound is the air coming out of the Trump inevitability balloon.

If Republicans can set aside their mystifying fascination with Mr. Trump, who has no consistent political ideology, it could set up a monumental primary fight for the soul of the party between Sen. Cruz and Sen. Rubio, or whoever emerges as the establishment choice.

The Cruz campaign showed its organizational strength in Iowa. Sen. Cruz is well funded and has his ground game established in the primary states to come. He is a good politician.

But as noted earlier in this editorial, his politics are extreme. Sen. Cruz would hurl the country back to a pre-New Deal United States, eliminating the departments of Education, Energy, Commerce, Housing and Urban Development, and the Internal Revenue Service. Sen. Cruz claims no IRS will be necessary to administer his flat tax of 10 percent on individuals and 16 percent on businesses.

Such a tax would be unfair, asking the rich to carry no greater proportional burden than the working class. And it would mean the loss of trillions of dollars in revenue, though this would suit Sen. Cruz fine. He wants to tear down the federal government and eliminate the jobs of hundreds of thousands of federal workers.

Sen. Cruz sees abortion and gay-marriage rights, as well as the concept of separation of church and state, as the product of “extreme leftists, activist judges, the Obama administration and academic elites” and would seek the appointment of Supreme Court justices to reverse judicial precedents supporting those rights.

Though he has tacked to the right in the nomination race, Sen. Rubio is a far more pragmatic conservative in the mold of House Speaker Rep. Paul Ryan, the party’s vice presidential candidate in 2012. He would seek moderation of tax policy, the trimming of federal government and reform of welfare policies. Sen. Rubio is far better positioned to reach beyond the conservative base in a general election.

On the Democratic side, the political pragmatists must be alarmed by the poor showing of former Secretary of State Hillary Clinton, who essentially ended in a caucus tie with the democratic socialist Sen. Bernie Sanders. He has tapped into anger among progressive Democrats who feel the party has been too cozy with a system that has seen wealth increasingly shifting to a privileged super-rich class while the middle-class shrinks and struggles.

Democrats acting with their hearts back Sen. Sanders, those with their heads, Ms. Clinton. The emotion and the excitement is on the side of Sen. Sanders. But though he can prolong the fight, it is hard to see a path to the nomination for the Vermont senator. And his own brand of extremism (by U.S. standards) — breaking up the banks, expanding social service programs, providing free college tuition, installing a national health care system — would not play well in a general election. He has already pulled Ms. Clinton left.

If Ms. Clinton indeed prevails, many Democrats, particularly young people, could be left disillusioned and unenthusiastic, making the party vulnerable to a moderate Republican. But will the GOP nominate one?