“There are some people who feel strongly” that Mr. Buttigieg has “not properly courted the African-American community,” said Ms. Neal, who endorsed Mr. Biden.

She attended a brunch on Sunday hosted by the Black Legislative Caucus, where Mr. Buttigieg told the room about his Douglass Plan to end institutional racism. He seemed to draw little attention from the 200 guests, who chatted and served themselves at a buffet.

Attendees mentioned Mr. Buttigieg’s lack of experience as the 38-year-old former mayor of a small city, as well as news accounts of opposition he faced by some black residents of South Bend.

In Nevada, Mr. Buttigieg’s message and strategy are similar to what worked for him in Iowa: Organize and travel widely, especially in areas where Democrats don’t often compete. On Monday, he campaigned in Elko, a deeply Republican region. He drew 300 people, but the effort may pay small dividends: Only 88 county delegates were selected in 2016 in all of Elko County, out of about 12,000 statewide.

Democratic voters are overwhelmingly concentrated in just two places: Clark County (Las Vegas) and Washoe County (Reno).

While Mr. Biden has attacked Mr. Sanders in recent days, and Mr. Sanders has rounded on Mr. Bloomberg, Mr. Buttigieg has stood largely apart from the fighting. On Tuesday night, his campaign announced that on Wednesday he would join members of Nevada’s powerful Culinary Workers Union, which declined to endorse a candidate, in a picket outside the Palms Casino.

Except for the faintest of swipes at Mr. Sanders in a TV ad here — saying Democrats can’t defeat Mr. Trump by “overreaching” — Mr. Buttigieg has portrayed himself as welcoming independents and “future former Republicans.”