Sen. Elizabeth Warren is taking the first formal steps toward a presidential candidacy. That includes a new 4½-minute video that ought to remind everybody why she became a progressive hero in the first place ― and why, despite her liabilities, she remains such a formidable contender for both the Democratic Party nomination and the presidency itself.

The reminder is necessary because the last few months have been rough for Warren, the Democrat from Massachusetts who first won election to the Senate in 2012. The trouble started in October when she tried to defuse the controversy over her past claims of Native American ancestry by taking a DNA test and producing yet another video, this one featuring relatives vouching for her side of the story.

The test and testimonials actually backed up her repeated statements that, as a child, she’d been told she had a Native American ancestor. They came on the heels of an exhaustive Boston Globe investigation showing that claims of Native heritage had played no role in Warren’s getting law faculty positions at the University of Texas, the University of Pennsylvania and Harvard.

Even so, Warren ended up angering Native American activists and provoking a new round of “Pocahontas” mockery from President Donald Trump, creating a media scrum that raised new doubts about her political judgment rather than quelling old ones about her ancestry and honesty.

Every person in America should be able to work hard, play by the same set of rules, & take care of themselves & the people they love. That’s what I’m fighting for, & that’s why I’m launching an exploratory committee for president. I need you with me: https://t.co/BNl2I1m8OX pic.twitter.com/uXXtp94EvY — Elizabeth Warren (@ewarren) December 31, 2018

Meanwhile, many of the progressives who had urged her to run in 2016 had since become more excited about Sen. Bernie Sanders, the Vermont independent who ultimately did challenge Hillary Clinton for the Democratic nomination. Other voters in the party seemed increasingly interested in younger, less familiar candidates, such as Beto O’Rourke, the Democratic congressman from Texas who came surprisingly close to ousting Republican Sen. Ted Cruz.

Since then a series of polls has shown Warren falling in the Democratic pack, despite her high name-recognition and familiarity to politically informed voters. And although early polls are notoriously misleading, one problem for Warren is the questions some progressives have about her electability. As much as they may support her positions, they worry that she will come off as too liberal or maybe too shrill ― an adjective, they know only too well, that voters apply selectively to women.

These are not crazy thoughts. Warren really does have some serious political liabilities. But it’s an open question just how much those liabilities would matter at the polls ― and Democrats should know this better than anybody, just based on recent history.

Five different Democrats have run for president since 1992, and the two that won carried massive, potentially fatal vulnerabilities into their campaigns. For Bill Clinton, the problem was accusations of philandering and serial dishonesty at a time when those characteristics were considered at least somewhat disqualifying. For Barack Obama, it was darker skin and a Middle Eastern-sounding middle name at a time when (as now) racism remained among the most powerful forces in politics.

Their eventual electoral success, despite these weaknesses, had a lot to do with the political environments in which they first sought the office. If you want to challenge a president, it helps to campaign when the economy is struggling. But what ultimately allowed Clinton and Obama to succeed were their electoral assets ― including their charisma and eloquence, their superior campaign organizations, and ultimately their ability to carry a message perfectly suited for the political moment and the opponents they faced.

The same was not true of Al Gore, John Kerry or Hillary Clinton. They were experienced and smart, for sure, but they had ambiguous political identities and reputations, deserved or not, of altering their positions to match the public’s ever-changing moods. They could deliver speeches competently but couldn’t do so with passion. They could command respect, for the most part, but they could not generate affection.

So on which list does Warren belong? It’s impossible to say right now, but there are plenty of reasons to believe that, like Obama and Bill Clinton, she’s the type of candidate with enough strengths to overcome her weaknesses ― especially given the man she would be running to replace.

Arguably two of Trump’s biggest vulnerabilities are his history of personal corruption and his pursuit of the traditional Republican economic agenda, which showers benefits on corporations and the rich while taking away programs and supports for everybody else. A Democrat with a strong record of fighting corruption could exploit the corporate largesse. A candidate with a strong record of fighting for the middle class and poor could exploit the weakening of the safety net. Warren happens to be both.

As the campaign video reminds viewers, she first became a political headliner by attacking banks for taking advantage of unsuspecting poor and middle-class customers. She can legitimately claim credit for developing the idea of a new government agency to protect consumers and then lobbying for it until it became reality. She can also take some credit for pushing the entire political discussion about the finance industry in a more progressive direction.

It helps that Warren is a bona fide policy wonk who long ago worked out her own political identity and her own preferred ideas on many key issues. That might not sound like a big accomplishment, but surprisingly few politicians have done the thinking and research it takes. Even among the ranks of serious presidential contenders, it’s not easy to find candidates who can articulate exactly why they want to be president, beyond the mere pursuit of power, and what they’d actually do if they were to win.

Warren has a few other things going for her, too. They include a compelling, impressive biography of facing and then overcoming challenges familiar to so many Americans ― like growing up in a family that teetered on the edge of financial catastrophe or struggling, as a working mom, to find decent child care that she could afford.

The video emphasizes this, showing old family photos of her with her children. It’s an almost-perfect juxtaposition to Trump, who became rich and reportedly avoided the Vietnam draft because of his father’s wealth and connections ― and who probably never changed a diaper in his life. (Trump famously has derided men “who act like the wife.”)

Whether all of this is enough to make Warren the Democrats’ best candidate, obviously, is another question entirely. The reality is that many of the Democrats intent on running have significant strengths. They also have significant weaknesses, which Trump would exploit just as surely as he has Warren’s.

Democratic primary voters will have to judge for themselves which candidate is most likely to win and which has the most to offer as a potential president. But an awful lot of people wanted Warren to run back in 2016, and the qualities that made Warren attractive then would seem, if anything, to be even more relevant now.