But there are other reasons for the discomfort with Mr. Ellison that illustrate lingering divisions after a bruising presidential primary fight and a general election in which Hillary Clinton suffered deep losses among working-class whites and could not match Mr. Obama’s support among young and nonwhite voters.

Some Democrats, in Mr. Obama’s orbit and beyond, say that elevating Mr. Ellison would amount to handing the party to Senator Bernie Sanders of Vermont, Mrs. Clinton’s primary race opponent, and his liberal followers.

Mr. Ellison was a high-profile backer of Mr. Sanders’s presidential campaign, and Mr. Sanders has been rallying support for Mr. Ellison’s D.N.C. bid. Already a polarizing figure among Democrats, he ignited new controversy this week by saying the party needed to “go beyond identity politics.”

“It’s not good enough for someone to say: ‘I’m a woman! Vote for me!’” Mr. Sanders told students in Boston on Sunday, a comment widely seen as a criticism of Mrs. Clinton. “No, that’s not good enough. What we need is a woman who has the guts to stand up to Wall Street, to the insurance companies, to the drug companies, to the fossil fuel industry.”

This call for an economic-centered brand of liberalism is what galvanized so many of his supporters, but his blunt language also served to remind some Democrats of the divisive primary race. There is little appetite for a replay of that fight in the D.N.C. race, which will be decided by members of the committee when they gather in February for their winter meeting.

Some top Democrats had hoped to pre-empt a contest by backing Mr. Ellison’s bid. Mr. Schumer, Ms. Warren and an array of House members and unions were lining up behind him even before he formally entered the race.