Beyer stresses that he's not pushing for an endorsement right now — just for lawmakers to pay attention to Buttigieg.

"I do not ask for your commitment to the Buttigieg candidacy," Beyer wrote. "Rather, I do hope you will keep an open mind as the campaign unfolds.”

Beyer’s letter is part of a broader push by Buttigieg’s campaign to gain a foothold among black Democrats in recent weeks, including a recent listening tour in South Carolina. But the fact that the letter is coming from a white congressional supporter is emblematic of the South Bend, Ind., mayor’s troubles. His polling among black voters continues to scrape the low single digits even as he has joined the pack of front-runners in largely white Iowa and New Hampshire. In a November poll of South Carolina voters conducted by Quinnipiac, Buttigieg received zero support from black voters.

Meanwhile, black voters and activists have condemned parts of Buttigieg’s mayoral record, and he has faced criticism that his campaign padded lists of supporters of the Douglass Plan with people who weren’t backing it or his campaign.

Rep. Don Beyer. | AP Photo

Skepticism persists among members of the Congressional Black Caucus: One black lawmaker who is considering supporting Buttigieg said that whenever Buttigieg’s name comes up in CBC meetings, most members argue that the Indiana mayor from a town of 100,000 people doesn’t stand a chance beyond Iowa.

But some black leaders are open to Buttigieg: Rep. Anthony Brown, a moderate black Democrat from Maryland, is being courted by the Buttigieg campaign and said he is planning to meet the candidate in person soon. He is aiming to endorse a presidential candidate in the next month.

“I like his positions on issues, particularly on national security, he's very thoughtful,” Brown said of Buttigieg. “I like him, I like Biden as well.”

Buttigieg’s supporters recognize that it’s critical he begin to break in with black voters if he is to actually contend for the Democratic nomination.

"You see how wonderful he's doing in Iowa and New Hampshire at the moment and how terrible he's doing relatively in South Carolina, largely because his support among African Americans approaches zero,” Beyer said in an interview. “If he's going to be a viable candidate for the middle run and the long run, he has to be able to expand the base to include a strong African American support. From my perspective, there's no reason he couldn't be able to do that or shouldn't be able to do that.”

“There's some white politicians for whom it's going to come easily than for others,” Beyer added. “It hasn't come easily for Pete.”

Buttigieg's campaign did not respond to a request for comment.

Rep. Marcia Fudge (D-Ohio), who supported Sen. Kamala Harris’ presidential bid, has spoken to Buttigieg and said she’d likely endorse a candidate again before the Iowa caucus. But Fudge took issue with the coverage Buttigieg has received, asserting that the media has given him “a pass.”

“They fawn all over him because he went to see Rev. [William] Barber,” Fudge said, referring to a recent visit Buttigieg made to Barber’s congregation in North Carolina. “How many black people in his own city does he talk to, in a city that’s 25 percent black?”

Some, however, are staying open to the young candidate. Rep. Robin Kelly (D-Ill.) recently introduced Buttigieg at a CBC retreat.

And one CBC member, who requested anonymity to speak more freely about their endorsement thinking, called Buttigieg a “knowledgeable” and “respected candidate.”

"Apparently, he's making a legitimate effort to establish a relationship with the African American community,” said the member. “He hasn't had one to this point, but he's trying."