By Peter Nicholas 

DES MOINES, Iowa--A schism is emerging among Democrats over the party's economic message, pitting those who favor policies that foster broad economic growth against others rallying behind Sen. Elizabeth Warren's call for a focus on income inequality.

Ms. Warren's growing prominence on the national stage has fed the debate, with her supporters pressing her to run for the Democratic nomination in 2016 to elevate issues such as corporate influence and the share of wealth controlled by the nation's richest households.

The liberal advocacy group MoveOn.org hosted an event in Iowa on Wednesday night aimed at showcasing support for Ms. Warren in the state that holds the nation's first presidential contest. MoveOn also plans to spend $1 million on its "Draft Warren" effort and is hiring staff in Iowa, New Hampshire and possibly other states that hold early primaries.

It seems doubtful at this stage that Ms. Warren will go along. She has said she is backing former Secretary of State Hillary Clinton, telling National Public Radio earlier this week, "I am not running for president." Yet in sticking to the present tense, as NPR's Steve Inskeep pointed out, she suggested she hasn't entirely ruled it out.

As they eye Ms. Warren's rising profile, some Democrats are warning that broad swaths of voters will reject her focus on economic inequality. "In a world where there are more self-described conservatives than there are self-described liberals, is having a campaign that only tries to win by appealing to your base the right strategy?" asked Jack Markell, the Democratic governor of Delaware. "I would argue it's not."

Mr. Markell, who hasn't yet endorsed a candidate for the 2016 election, said the next Democratic nominee has to reach independents and "some Republicans, as well. In my mind, an agenda around [economic] growth is the most likely message to do that."

Unclear amid the debate is what tone and policy profile Mrs. Clinton would adopt should she run for president. Just as Ms. Warren, a Massachusetts senator, has come to symbolize the Democrats' liberal wing, Mrs. Clinton is rooted in the ranks of business-friendly centrists, many of whom believe Warren-style populism is a risky electoral strategy.

For years, the liberal and moderate strands of the party largely minimized differences and kept a united front amid Republican resistance to President Barack Obama's agenda. But the uneasy alliance has become strained after the midterm elections, in which the party suffered deep losses.

A sign of the split is stepped-up calls for Ms. Warren to jump in the presidential race. Some 300 lower-level former Obama campaign aides are lining up behind the Massachusetts senator, signing a recent letter describing her as someone who would "take on the Wall Street banks and special interests" and tackle "rising inequality," which they called the "challenge of our times."

A liberal advocacy group called Democracy for America is sinking $250,000 into the effort to draft Ms. Warren. Yet the group's founder, former Vermont Gov. Howard Dean, has endorsed Mrs. Clinton.

Ms. Warren gained fresh attention last week, mounting an unsuccessful campaign in the Senate to scuttle a provision in a $1.1 trillion spending bill that will loosen parts of the Dodd-Frank financial-regulation law that passed in Mr. Obama's first term.

In her attempt to do away with the provision, she employed the sort of language that leaves liberals enthralled and centrists unnerved. Taking aim at Citigroup Inc., a recipient of taxpayer-financed bailout money during the financial crisis, Ms. Warren said in a speech on the Senate floor: "Washington already works really well for the billionaires and the big corporations and the lawyers and the lobbyists. ...What about the families who are living paycheck to paycheck and saw their tax dollars go to bail out Citi just six years ago?"

Ms. Warren decried what she cast as a revolving door between Citi and the top ranks of the U.S. Treasury Department, saying the bank has too much political and economic clout.

"We're at a crossroads: The rich the ones at the very top are getting wealthier and wealthier," Ilya Sheyman, executive director of MoveOn, told roughly 100 people at the event in Des Moines. "The middle class and those struggling to get into it are falling further and further behind....This is a moment for Elizabeth Warren."

Those aligned with Ms. Warren call for policies that would increase the minimum wage, raise taxes on wealthy households and subject Wall Street firms to tighter regulation.

While embracing some of those goals, others in the party tout policies that would strengthen education, improve roads and bridges, and promote exports. And they describe businesses as more of a partner in a joint endeavor to expand economic opportunity than a special interest to be tamed.

In the midterm elections, many Democrats made a minimum-wage increase the centerpiece of their campaigns. Rep. John Delaney (D., Md.), who has warned against rhetoric that winds up "demonizing the private sector," said the message must be more encompassing.

"You cannot anchor your whole economic message around" the minimum wage, he said, "because in fact it doesn't affect a lot of Americans, and it doesn't get at the heart of the issue: Creating more middle-skill jobs where people can have a decent standard of living and feel like their kids have opportunity."

In her recent book, "Hard Choices," Mrs. Clinton wrote about her efforts as secretary of state to boost exports and help U.S. businesses gain access to foreign markets, in the interest of creating jobs at home.

At the same time, she has begun sprinkling her speeches with populist themes. "Our democracy is supposed to work for everyone, not just the privileged few," Mrs. Clinton said this fall at a campaign appearance in Kentucky. "But, more and more--you know this, you feel it, you live it--the scales are weighted against working families."

Mrs. Clinton also has been hinting that she would like to bridge the divide between the party's left and centrist blocs. "I love watching Elizabeth giving it to those who deserve to get it," she said at a campaign rally in October for former Massachusetts Democratic gubernatorial candidate Martha Coakley.

Janet Hook contributed to this article.