Some progressives want Sen. Bernard Sanders of Vermont on the Democratic presidential ticket and won’t be fully satisfied with anyone else as Hillary Clinton’s No. 2 — not even fellow anti-Wall Street crusader and liberal firebrand Sen. Elizabeth Warren.

Ms. Warren has emerged as a top contender to be Mrs. Clinton’s running mate, but data show that picking the senator from Massachusetts won’t necessarily lead liberals to coalesce around Mrs. Clinton and would have little impact on independent and moderate voters.

On the surface, the case for choosing Ms. Warren seems straightforward. Mrs. Clinton needs to woo progressives who backed Mr. Sanders in the primaries yet remain skeptical of her candidacy, and the anti-Wall Street message of Mr. Sanders is strikingly similar to that of Ms. Warren. Mrs. Clinton and Ms. Warren recently appeared on the campaign trail together and have had glowing praise for each other in recent weeks. Ms. Warren also has become a fixture in Clinton campaign emails and social media outreach.

But picking Ms. Warren to placate frustrated, disillusioned Sanders supporters probably wouldn’t work, political analysts say, and would do little to boost Mrs. Clinton’s chances of beating Republican rival Donald Trump in November.

“There is a growing sense that Sanders supporters see this as a token pick, which would not help Clinton in the end,” said Brandon Rottinghaus, an associate political science professor at the University of Houston. “When you think about a vice president choice, you’re trying to balance out your weaknesses, so she needs to think carefully about where her weaknesses are and accommodate that more than thinking about the short-term need to unify the party following a bitter primary fight.”

Indeed, some angry Sanders supporters who seem unable or unwilling to support a Clinton-led ticket have labeled Ms. Warren a “sellout” on social media.

For those voters, even the inclusion of Ms. Warren won’t be enough. More broadly, a clear majority of Democrats think Mrs. Clinton should choose someone else, whether that be Mr. Sanders or another Democrat.

A CNN/ORC International poll conducted last month found that 34 percent of Democrats say Mrs. Clinton should choose Ms. Warren as her running mate. Fifty-four percent said she should pick someone else, and 11 percent had no opinion.

Among Democrats, 38 percent say putting Ms. Warren on the ticket would make them more likely to support Mrs. Clinton in November. Eleven percent said it would make them less likely, and 45 percent said it would have no impact, according to a recent Monmouth University poll.

But that same poll found that 53 percent of Democrats would be more likely to vote for Mrs. Clinton if Mr. Sanders is on the ticket. Among independents, 44 percent said they would be more likely to vote for the Democratic ticket if Mr. Sanders is on it, compared with 25 percent who said that of Ms. Warren.

In fact, 22 percent of independents said Ms. Warren would make them less likely to vote Democratic, and 49 percent said it would have no impact, meaning that picking the senator from Massachusetts essentially would be a wash among that crucial bloc of voters.

Although some of those independent voters have been drawn to the populist pitches of Mr. Sanders and Ms. Warren, many of them — particularly those in swing states such as Ohio and Pennsylvania — may be more comfortable with a moderate Democrat on Mrs. Clinton’s ticket, said Matthew Dallek, an assistant professor of political management at George Washington University.

“Beyond the Wall Street issue, [picking Ms. Warren] probably does make it harder to reach out to more centrist voters and some independents,” Mr. Dallek said.

Ms. Warren also simply wouldn’t attract liberals in the same way Mr. Sanders would. The Monmouth poll found that 64 percent of voters who identify as liberal say they would be more likely to vote for Mrs. Clinton if Mr. Sanders is on the ticket. Just 48 percent said the same of Ms. Warren.

Other potential vice presidential picks — such as Sen. Tim Kaine of Virginia, Sen. Cory A. Booker of New Jersey, Labor Secretary Thomas E. Perez and others — move the needle much less than Ms. Warren, yet there is no doubt Mr. Sanders is the most popular choice by virtually every measure, including fundraising.

Iowa-based polling company RABA Research released a survey last month asking Democrats which candidate would make them more likely to give money to the Clinton campaign. Mr. Sanders came out on top with 35 percent, though Ms. Warren was close at 30 percent.

Regardless, adding Ms. Warren to the ticket could be the best way — short of choosing Mr. Sanders himself, which seems to be a far-fetched proposition — to bring at least some disenchanted progressives back into the fold. Even some Republicans say a Clinton-Warren ticket would unify the Democratic Party.

“She’s captivating. She is really smart,” Sen. Mike Lee, Utah Republican, recently said of Ms. Warren. “And I believe she is kind of a hero among a lot of people in the Democratic Party, including a lot of people who have been big fans of Bernie Sanders. So, I suspect that would be a strong play if Hillary Clinton were to go in that direction.”

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