Can Elizabeth Warren Elizabeth WarrenDimon: Wealth tax 'almost impossible to do' CNN's Don Lemon: 'Blow up the entire system' remark taken out of context Democrats shoot down talk of expanding Supreme Court MORE win back blue-collar Democrats from President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE in Michigan, Wisconsin and Pennsylvania?

It’s a question many Democrats are pondering as Warren — one of the leading contenders for her party’s presidential nomination, if she chooses to run in 2020 — goes back and forth with the president over immigration and other issues.

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Warren (D-Mass.) has shown an ability to rally and excite progressives, she’s a proven fundraiser and she has policy bona fides from her work in the Senate.

Yet there are creeping doubts among some Democrats that she’s the best candidate to take on Trump.

Some worry the former Harvard professor will have a tough time winning back the Rust Belt centrists and independents who abandoned Hillary Clinton Hillary Diane Rodham ClintonDemocratic groups using Bloomberg money to launch M in Spanish language ads in Florida The Hill's Campaign Report: Presidential polls tighten weeks out from Election Day More than 50 Latino faith leaders endorse Biden MORE and Democrats for Trump.

“I just can’t see a blue-collar, Rust Belt guy voting for her,” said one Democratic strategist who has worked on presidential campaigns. “I think the party needs to be realistic about that.”

Some Democrats almost certainly remain shellshocked from the last election after Trump’s surprise win. He became the first Republican to win the states of Pennsylvania and Michigan in a presidential election since 1988 and the first Republican to win Wisconsin since President Reagan in 1984.

If Democrats don’t retake those states in 2020, their chances of winning the Electoral College will fall.

Teeth-gnashing over who is best-positioned to take on Trump, as a result, is already taking place ahead of the midterm elections.

Warren’s gender and her political identity as a voice on the left are both likely to be issues for primary voters sizing up Democratic candidates in potential head-to-head matchups with Trump. Would she be stronger than former Vice President Joe Biden Joe BidenBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Democratic groups using Bloomberg money to launch M in Spanish language ads in Florida Harris faces pivotal moment with Supreme Court battle MORE? What about Sen. Bernie Sanders Bernie SandersOutrage erupts over Breonna Taylor grand jury ruling Dimon: Wealth tax 'almost impossible to do' Grand jury charges no officers in Breonna Taylor death MORE (I-Vt.)? Does the party need the face of a new political generation, such as Sens. Kamala Harris Kamala HarrisHarris faces pivotal moment with Supreme Court battle Nearly 40 Democratic senators call for climate change questions in debates Joe Biden has long forgotten North Carolina: Today's visit is too late MORE (Calif.), Cory Booker Cory Anthony BookerBipartisan praise pours in after Ginsburg's death DHS opens probe into allegations at Georgia ICE facility Democratic lawmakers call for an investigation into allegations of medical neglect at Georgia ICE facility MORE (N.J.) or Kirsten Gillibrand Kirsten GillibrandSunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Suburban moms are going to decide the 2020 election Jon Stewart urges Congress to help veterans exposed to burn pits MORE (N.Y.)?

Warren has her advocates, who say the senator’s anti-corporate economic message will resonate with the types of voters who left the party for Trump.

Jesse Ferguson, who served as a spokesman for Clinton’s 2016 presidential campaign, said Warren “has a powerful economic message that resonates everywhere.”

Democratic pollster Celinda Lake said Warren is the perfect candidate to oppose Trump because she “has the ability to go straight at him on his economic policies.”

She also argued that Trump’s repeated attacks on Warren suggest the White House sees her as a threat.

“I think this man understands his brand very well and understands his populist appeal very, very well, and he realizes how threatening to him she is on his brand,” Lake said.

Warren’s office declined to comment for this story.

Trump mocked Warren over her Native American heritage twice last week, once on Twitter but also at a campaign-style rally.

“Let’s say I’m debating Pocahontas. You know those little [DNA] kits they sell on television for two dollars? … I’m going to get one of those little kits and in the middle of the debate when she proclaims that she’s of Indian heritage, because her mother says she has high cheekbones,” Trump said to the cheering crowd in Montana.

“We will take that little kit … but we have to do it gently because we are in the ‘Me Too’ generation,” Trump said, adding that he would donate $1 million to Warren’s favorite charity if she took the DNA test. “I have a feeling she will say no.”

Warren immediately hit Trump back on Twitter.

“Hey, @realDonaldTrump: While you obsess over my genes, your Admin is conducting DNA tests on little kids because you ripped them from their mamas & you are too incompetent to reunite them in time to meet a court order. Maybe you should focus on fixing the lives you’re destroying,” she wrote.

Warren called Trump a bully during an event outside Boston over the weekend.

“He tries to bully me in order to shut me up,” Warren said, according to the Boston Herald. “I seem to be in his head.”

Warren is a favorite of liberals and could be well-positioned to win her party’s nomination given the ascent of the liberal wing.

“She has a very strong base of support and is one of the few figures on the left who has a chance at winning over a broader range of the party,” said Julian Zelizer, a professor of history and public affairs at Princeton University.

He said her focus on consumers and the middle class is the kind of rhetoric that resonated with Sanders supporters in 2016.

Zelizer said the question, if she wins the nomination, is whether she “can withstand what will certainly be a brutal general election campaign against the master attacker.”

Warren’s counterattacks on Trump could be read as sending the message to prospective Democratic primary voters that she’s more than up to that task.

Another factor for Warren is whether some segments of the Democratic electorate see her as too liberal to defeat Trump.

Basil Smikle, a Democratic strategist who served as the executive director of the New York state Democratic Party, said he’s not sure Warren could woo independents.

“Democrats are certainly motivated on issues like [Immigration and Customs Enforcement] separating children and the potential for the Supreme Court to reverse Roe v. Wade, but are independents that upset?” said Smikle, who worked for Clinton. “They may not like Trump’s tactics, but they may, to some extent, like the ultimate outcome if it helps to stem the tide on undocumented workers.”

But Lake argues that Warren would strike directly at independents because of her populist approach.

“In some ways, she’s Trump’s worst nightmare for independents,” she said. “She can run rings around him.”