And even as he has become the darling of the limousine liberal, NPR crowd , a status that will no doubt be reflected in his next fundraising haul, Buttigieg appears to be stuck in neutral.

His latest poll numbers show him at 6%, down from 8% a month ago, but up from 1% in March, according to a recent Monmouth University poll

Yes, it's early. But the question for Buttigieg, who was featured on the cover of Time magazine and has been on a steady town hall and media blitz, is where are his possible avenues of growth among Democratic voters?

The central argument of his candidacy is that he has a unique appeal to a broad array of voters in the Midwest, specifically white working-class voters.

The problem with that argument is Buttigieg has shown no evidence that he can actually do that -- South Bend is a liberal-leaning college town that has had a Democratic mayor since 1972. His only state-wide run -- a 2010 state treasurer bid -- ended in defeat. And so far, nothing in the polling suggests that he has a particular appeal among white voters of any socioeconomic status.

The news isn't any better for Buttigieg among African-American, Latino and Asian-American voters who make up about 40% of the Democratic base.

Of course, African-American voters will be a critical voting block in southern states, where they will make up as much as 60% of the primary electorate.

His biggest problem in gaining ground with this constituency (and every constituency) is Joe Biden

Buttigieg has been meeting with prominent African-Americans, among them Al Sharpton and South Carolina Rep. Jim Clyburn. He has also been meeting privately with others, one of whom described him as frustrated that he wasn't doing better in the early polling among African-Americans.

In a trip to South Carolina, which drew few African-American voters, he made an open call for African-Americans to join his campaign, though it was unclear what he was actually asking black voters to do. Vote for him, work for his campaign, volunteer for his campaign?

Since then, the campaign has hired Nina Smith, a former Obama administration official and Rep. Maxine Waters staffer to serve as traveling press secretary. Rodericka Applewhaite is his rapid response director. But as we've seen in previous campaigns, staff hires and endorsements, no matter how high-profile, can only go so far.

A question that southerners often have when they meet someone is -- who are your people? The question is, of course, about family ties, but it's another way of asking who someone is, where they're from, and whether there are any important connections.

It's a useful way of thinking about how some black voters will view this field. For Biden, the answer is, he worked side by side with Barack Obama. Bernie Sanders has been citing his ties to Jesse Jackson and Martin L. King, to limited effect. Kamala Harris, the daughter of civil rights activists raised in Oakland, is a Howard graduate, and member of Alpha Kappa Alpha, an African-American sorority. Elizabeth Warren, clearly aware of her weaknesses among African-American voters, talks more about racial inequality than any other candidate, and her economic policies reflect it.

At a Washington Post event this week, Buttigieg, asked how he can make up ground among African-American voters, cited a broad black agenda, but said he still had work to do in getting his name out there. After the event, I asked a black woman, who is lobbyist but declined to be named because of her job, what she thought of Buttigieg. She shrugged, clearly unimpressed.

"I'm tired of people having to get up to speed on our issues," she said. "Why does there have to be on-the-job training when it comes to us?"