WASHINGTON — What's the biggest beef against Sen. Elizabeth Warren, who is considering a run for president against Donald Trump?

It's that she's "too divisive," an argument put forward by her hometown newspaper, The Boston Globe, in a widely discussed editorial last week urging her not to run for president. It sparked both public rebukes of the paper and some private nods of agreement from Democrats as they begin to consider in earnest what kind of person their party should put up against Trump in 2020: a fighter, a friendly face or some combination of both?

"Democrats will be looking for someone who can float like a butterfly and sting like a bee," said Matt Sinovic, the executive director of Progress Iowa. "The nominee will have to point out Trump's many (many) failures and lies in a compelling way, fire up the base — all while reaching persuadable voters as well."

Warren entered the Senate five years ago with an unusually high profile and was polarizing from the start. She built a national base of super fans, including almost 15 million followers on social media, but also a dedicated cadre of detractors — a few within her own party and more among conservatives, including the current occupant of the Oval Office.

"She's always been divisive and she's as divisive as she's always been when you look at her poll numbers," said Massachusetts pollster Steve Koczela, the president of the MassINC Polling Group. "She's been very strongly liked by Democrats and very strongly disliked by Republicans, since her first election."

Warren's confrontational exchanges with Trump on Twitter and eagerness to call out villains like Wall Street banks have put a big target on her back and carved an image of her that might be difficult to alter in the heat of a presidential campaign.

That was made clear this fall when Warren tried to finally put to rest lingering questions about her Native American heritage by releasing the results of DNA test, only to see it backfire and spark new criticism of her from both the right and left.

After watching their party win the House with a message that largely ignored Trump, some Democrats now seem more interested in a fresher face more likely to turn the other cheek, try to stay above the fray, and focus on policy. Rep. Beto O'Rourke, D-Texas leapfrogged Warren and others in a new CNN poll of the nascent 2020 field.

On the flip side, however, many Democrats saw the Globe's editorial as proof that Warren is getting "Hillary-ed," as feminist author Rebecca Traister put it last year — held to a different standard than her male counterparts in a way that risks sucking her into a vicious cycle where attacks lead to pundits' concerns about her divisiveness, which in turn prompt more attacks, and so on.

"The thing that I am interested in watching is what happens in a field with multiple women candidates, because we have never seen that before," said Jess McIntosh, a veteran of Clinton's 2016 campaign who now edits the progressive website ShareBlue. "It will be a lot easier to ferret out double standards and gendered attacks."

After all, Warren was the name most often mentioned by progressive who said in 2016 that they'd like to support a female candidate other than Clinton. What happens now that they might actually get a chance to back Warren?

"When that becomes, 'I would be happy to vote for a woman candidate — just not that one, or that one, or that one or that one,' then it becomes a little more obvious what's going on," McIntosh said. "It's rare that you see the word divisive applied to a male candidate."

Anyone who mixes it up with Trump, as the Democrats eventual nominee will have to, is bound to wind up with a black eye or two, and Warren has taken more incoming fire from Republicans than most of her potential Democratic rivals. Her defenders say Warren's proven she can withstand it.

For instance, the GOP opposition research super PAC America Rising singled out Warren in early 2017 to be the target of an early effort to "make life difficult" for potential presidential candidate.

"They're all gonna be 'divisive' by 2020," tweeted Adam Jentleson, a former top aide to Senate Democratic Leader Harry Reid.

Still, Warren has made no apologies for picking more fights and cutting a sharper swath through Washington than many of her colleagues.

"I threw rocks before I ever got to this town and I'm not through throwing rocks now," she said in interview on ABC News a year before winning her first term in the Senate. "So if there are folks who don't like what I do, so be it, but I’m still ready to fight."

In her latest and pugilisticaly title book, "This Fight Is Our Fight," Warren wrote of that frequent Twitter scraps with Trump split even some friends: "Some people loved them; others winced."

"I figured that if tweeting and posting and poking and prodding gave me a chance to reach millions of people (with information about Trump's shady business history), then that's what I should do," Warren wrote. "And if the cost of taking a shot at the hot-air balloon known as @realDonaldTrump was that I had to take a few hits of my own, then so be it."

Back home in Massachusetts, the Globe noted that Warren is less popular than former Democratic Gov. Deval Patrick, who recently ruled out a 2020 bid, and current Republican Gov. Charlie Baker.

But Koczela noted that Massachusetts' track record at picking winning presidential candidates is not great -- just ask Mitt Romney, John Kerry, and Michael Dukakis.

"I just don’t think that how Massachusetts voters feel about someone is a good indicator of how they would do on the national stage," Koczela said.