DENVER—Minnesota Rep. Keith Ellison, who has campaigned hardest to become Democratic National Committee chairman, faces criticism from some fellow Democrats who object to having an elected officeholder in the job.

Without Democratic control of the White House or Congress, the party chairman must serve as chief spokesman—both in advancing Democratic positions and attacking Republicans—while also devising strategies for attracting swing and independent voters.

“When you do not have the presidency or control Congress, it’s a big job, a really heavy lift,” said Susan Swecker, chairwoman of the Democratic Party of Virginia. “This is such a heavy lift that it requires full-time attention. I hear that over and over.”

In this post-election period, many DNC members are also demanding a return to a “50-state strategy,” pioneered by former Chairman Howard Dean in 2005, to improve the party’s odds of recovering in many statehouses and legislatures where it has lost ground.

But that upsets the congressional wing of the party, because it risks draining resources from midterm elections in 2018, when many of the party’s senators are up for re-election, and weakening the battleground infrastructure for the 2020 presidential contest.

Mr. Ellison is set to appear at a two-hour forum here Friday with three other contenders to lead the party. The event will mark the first step in the party’s effort to rebuild itself after a cascade of GOP victories since 2010 that has driven Democrats from power both in Washington and in state capitols.

Mr. Ellison, an African-American who was the first Muslim elected to Congress, would showcase the party’s diversity during the Trump administration.

But he was also a top surrogate for the Vermont Sen. Bernie Sanders, the insurgent primary challenger to Hillary Clinton at a time when most DNC members were backing her. And his past statements about Israel and his writings backing such provocative figures as Nation of Islam leader Louis Farrakhan have become a ripe target for those who would like to block his path to the chairmanship.

“The United States foreign policy in the Middle East is governed by what is good or bad through a country of seven million people,” Mr. Ellison said at a 2010 fundraiser, the audio of which was published online this week by the Investigative Project on Terrorism, a website that largely carries conservative commentary. “A region of 350 million all turns on a country of seven million. Does that make sense? Is that logic? Right?”

Marcel Groen, the Pennsylvania Democratic Party chairman who is the son of Holocaust survivors, said he found those kind of remarks troubling. “Mainly for me, his view of the Israel-Palestinian issues, I want some clarity,” Mr. Groen said.

Rep. Nancy Pelosi was re-elected as House Minority Leader on Wednesday, but many in her party cast ballots for Rep. Tim Ryan. The election highlighted rifts in the party along geographic and ideological lines. WSJ politics reporter Janet Hook explains. Photo: AP

Of the four announced candidates for DNC chairman, Mr. Ellison has the highest-profile endorsements, including Mr. Sanders and Sens. Charles Schumer of New York and Elizabeth Warren of Massachusetts. The AFL-CIO, in an email to its executive council members, asked only if the labor federation should back Mr. Ellison or make no endorsement—it didn’t propose supporting any other candidate to lead the party.

The other three hopefuls currently seeking the reins of the party are Mr. Dean, South Carolina Democratic Chairman Jaime Harrison and New Hampshire Chairman Ray Buckley and an organization of Democratic state party chairmen. Labor Secretary Tom Perez and NARAL Pro-Choice America President Ilyse Hogue are considering running.

In an interview here on Thursday, Mr. Harrison said he would bring back Mr. Dean’s 50-state strategy, but present a fresh face for the party. “I’m New Age Howard Dean,” he said.

Mr. Ellison has been lobbying DNC members ahead of the Denver forum. He sent aides to meet party officials in Alabama and Mississippi this week and last week appeared himself at a meeting of the California Democratic Party’s executive committee.

Still, Mr. Ellison is encountering stiff resistance among rank-and-file DNC members who will select the party chairman.

His position as a sitting congressman rubs against those who believe that, without a Democratic president to lead the party, the DNC chairman should serve full time.

“This is even more demanding than what [former chairwoman] Debbie Wasserman Schultz faced, because we don’t have the president,” Ohio Democratic Party Chairman David Pepper said. “There are natural conflicts of interest that come up. It isn’t always going to align.”

Mr. Ellison’s defenders note that the last two DNC leaders, who were both selected by President Barack Obama, were elected officials who faced no opposition from the party at the time of their appointment.

“Some of these people have some nerve,” said Nina Turner, a DNC member from Ohio who was a chief surrogate for Mr. Sanders. “Gov. Tim Kaine was not full time, certainly not Debbie Wasserman Schultz.… I’m sensing some double standards here,” she said in a reference to the party’s former vice-presidential nominee and the Florida congresswoman who resigned in July.

Democratic skeptics of Mr. Ellison say his positions on Israel could be used to damage the party with Jewish voters and donors. Anti-Defamation League Chief Executive Jonathan Greenblatt on Thursday called Mr. Ellison’s past statements on Israel “both deeply disturbing and disqualifying.”

Mr. Ellison’s aides didn’t make him available for an interview, but provided a six-page document detailing his past support for Israel and Jewish causes.

“These are old attacks that the right wing has used to attack Keith’s character and work for the purpose of driving a wedge between Keith and the Jewish community,” the document states.

Friday’s forum is the first in a series of expected gatherings in which the DNC chairman candidates appear before and with party members. Interim DNC Chairwoman Donna Brazile said the party would hold regional forums in the new year for the chairman candidates to address and meet DNC members.

For Mr. Ellison, Friday’s gathering will serve as an opportunity to convince party members that he can bridge the various divides both within the party and about his own candidacy.

Roy Temple, the chairman of the Missouri Democratic Party, said Mr. Ellison needs to ensure he isn’t seen as just trying to “vindicate” the party’s Sanders camp by seeking the post.

“It should not be a prize someone seeks to vindicate this faction over another faction, filling a vacuum perceived to exist,” Mr. Temple said. Mr. Ellison, he said, “wants to do the right thing for our party. As part of his effort to do this, it’s important to indicate that is not what it is about.”