If we've learned anything in modern primaries, it's that winning begets winning.
His bigger obstacle could be Mike Bloomberg, who has Buttigieg soundly beat when it comes to mayoral records and net worth.
Having covered campaigns for a couple of decades, I've come to believe that some candidates are just get-to-yes candidates: Voters are looking for reasons to support them, because it feels ennobling. And the only question for the candidate is whether he or she can offer voters enough reassurance to make the leap.
Take, for instance, Barack Obama, whose age and lack of governing experience gave voters legitimate reasons, in both the 2008 primaries and in the general election, to choose someone else. They didn't, because Obama was a get-to-yes candidate; he made them feel good about themselves and the country. They found a way to overlook the rest.
For months now, a lot of Democrats have been telling us that Buttigieg inspires them. They love the idea of a Rhodes scholar with military credentials, a gay candidate who doesn't let identity define him, a candidate who came of age with social media and isn't pushing 80.
They just wish Buttigieg were even five years older or that he was the mayor of, you know, a real city. They'd like to be able to vote for him; it just seems like such a stretch.
But as we saw in Iowa, Buttigieg (who, full disclosure, was a friend of mine years before people started trying to pronounce his name) has given them enough reason to look past all that. He's lightning-quick on his feet, oddly self-confident, relentlessly disciplined and forward-looking. He's steadily getting them to yes, much as Obama did.
No one else in the field enjoys that advantage with voters who remain undecided at this stage.
Democrats have abiding affection for Biden, and they'd like to have got to yes with Biden, too, but as the Washington Post's Dan Balz noted in an incisive analysis, he's too slowed and too muddled to quiet the doubts.
Bernie Sanders, Vermont's socialist senator, polarises the Democratic electorate. If he wins, it'll be because enough candidates hang around to split the non-Sanders vote, in the same way that Trump won the Republican primaries with an unshakable plurality.
Elizabeth Warren, the populist Massachusetts senator, has given Democrats the kind of wonky agenda they claim to love. But to this point, anyway, undecided voters find her uninspiring.
I can't help thinking it's the way Warren blows through questions on the debate stage - the way she starts every single answer with "so ..." or "understand ...," as though she's hoping we can grasp this difficult concept, but let's be real, the odds aren't high - that pushes some voters away. Choosing Warren feels like signing up for a very long lecture just because you should.
I'm not saying Buttigieg has managed to neutralise all the doubts about his candidacy. He could probably stand to acknowledge those doubts a little more directly than he does.
As he did in a premature victory speech in Iowa, where he never even acknowledged the confusion surrounding the results, Buttigieg has a tendency to try to bluster his way through uncertainty rather than admitting what he can't or doesn't know. Maybe that creates an opening for a candidate such as Senator Amy Klobuchar of Minnesota, who manages to sound both self-assured and grown-up.
But it seems as though Buttigieg has gone a long way towards convincing sceptical Democrats that, like Obama, he has enough of an uplifting story and towering intellect to win over a crucial bloc of independent voters come November.
Trump is what you might call a get-to-no candidate - someone whom a lot of voters still find odious, even if they found a way to vote for him in 2016. They'd rather not do it again, if they can stomach the alternative.
All Democrats really need is someone who can get to yes.
