(CNN) Sen. Elizabeth Warren officially launched her 2020 presidential campaign Saturday at a rally in Lawrence, Massachusetts, using the backdrop of Everett Mills -- the site of a historic 1912 labor strike led by women and immigrants -- to issue a call to action against wealthy power brokers who "have been waging class warfare against hardworking people for decades."

Over 44 minutes in sub-freezing temperatures, Warren described a political elite "bought off" and "bullied" by corporate giants, and a middle class squeezed so tight it "can barely breathe."

"The man in the White House is not the cause of what is broken, he is just the latest and most extreme symptom of what's gone wrong in America," Warren said of President Donald Trump. "A product of a rigged system that props up the rich and powerful and kicks dirt on everyone else. So once he's gone, we can't pretend that none of this ever happened."

The formal start of Warren's White House campaign comes as the Democratic primary intensifies by the day, with numerous candidates including Sens. Kamala Harris and Cory Booker already in the race, and others, like Sens. Bernie Sanders and Amy Klobuchar, expected to jump in soon. Trump's 2020 campaign manager welcomed Warren to the race with a statement predicting voters "will reject her dishonest campaign and socialist ideas like the Green New Deal."

In a warning to some of those rivals, Warren touted her refusal to accept donations from lobbyists, corporate PACs or the support of super PACs, and challenged "every other candidate who asks for your vote in this primary to say exactly the same thing."

Warren also unveiled a new, high-profile backer in Rep. Joseph P. Kennedy III, who introduced, endorsed and painted his former professor a prescient political voice.

"Before there was an editorial every day lamenting economic inequity, Elizabeth Warren knew that stock prices don't tell a full account of our country's economic story," Kennedy said. "Medical bankruptcies and foreclosures and paychecks are part of that story, too."

Kennedy led a Massachusetts delegation that included Sen. Ed Markey, Rep. Lori Trahan, Lawrence Mayor Dan Rivera and Boston City Councilor Michelle Wu -- all of them indicating their support for Warren's campaign.

"For six years, (Warren) has been fighting in the trenches for what is right," Markey said of his Senate colleague, calling her a "one woman protection detail fighting to ensure that Wall Street reforms stay on the books."

Warren was joined by family, including her husband, Bruce, two children and a gaggle of grandchildren.

Kennedy's decision to throw his support to his home state senator -- and not his good friend, former Rep. Beto O'Rourke, who is considering a bid of his own -- is a clear signal to fellow Democrats that she remains a serious primary contender despite a politically trying week.

In the days leading up to Saturday's announcement, Warren had been weighed down by new questions over her past claims to Native American heritage. The Washington Post reported that Warren wrote in 1986 that her race was "American Indian" in a Texas state bar registration card, adding to the list of instances in which the senator self-identified this way.

The disclosure prompted yet another public apology from Warren, just days after she had expressed remorse to Cherokee leaders for using a DNA test last year to try to show her Native American ancestry.

A Monmouth University poll showed Warren get a boost in national support after she announced her exploratory campaign at the end of last year. But it's not yet clear whether the controversy's revival on Wednesday will hurt her standing with voters.

Warren sought to turn the page on the controversy with Saturday's announcement and a six-state tour that began hours later.

After Lawrence, Warren travels north to campaign in New Hampshire before flying to Iowa -- her second visit to the Hawkeye State since announcing the formation of an exploratory campaign on New Year's Eve -- on Sunday and then South Carolina, Georgia, Nevada and California next week.

The campaign's decision to stage its first major rally in Lawrence, a former industrial mill town, was an appeal to the key constituency groups Warren hopes to appeal to -- including immigrants, women, working class families and union members.

"There'll be plenty of doubters and cowards and armchair critics this time around," Warren said. "But we learned a long time ago, you don't get what you don't fight for."

In 1912, textile workers in Lawrence, many of them immigrant women, walked off the job and went on strike to protest wage cuts. In an email to supporters last week, the campaign wrote: "Underpaid, overworked, and flat-out exploited workers from more than 50 countries gave Lawrence the nickname 'Immigrant City.'"

Warren has been fiercely critical of the Trump administration's immigration policy, particularly in light of the separation of migrant children from their families at the border.

"I think we need immigration laws that focus on people who pose a real threat and I don't think moms and babies are the place that we should be spending our resources. Separating a momma from a baby does not make this country safer," Warren said in an interview with CNN last summer, a message she has returned to during her time on the campaign trail.

Two weeks ago, Warren added more meat to her platform, which already includes a suite of anti-corruption proposals -- on Saturday she called it "a cancer on our democracy" -- introducing a new "wealth tax" on Americans with assets valued at $50 million or more.

The plan, according to documents provided by the campaign, would impose a 2% tax on Americans whose net worth exceeds $50 million. Billionaires would pay an additional 1%. Viewed alongside a new proposal from Sanders to hike the estate tax, Warren has positioned herself at the center of the progressive push to reduce corporate influence in Washington and economic inequality across the country.

In her speech, she pledged to go further, to "break up monopolies when they choke off competition" and "take on Wall Street banks so that the big banks can never again threaten the security of our economy."

"And when giant corporations -- and their leaders -- cheat their customers, stomp out their competitors, and rob their workers," Warren said, "let's prosecute 'em."

But even as Warren sharpens her policy positions and political message, the specter of additional, previously undisclosed examples of Warren labeling herself Native American on professional forms looms in the background. Warren did not address the potential for another distracting revelation when asked by reporters on Capitol Hill this week.

Another unanswered question: whether the dust-ups will permanently undermine Warren's campaign. Tribal activists, who were sharply critical over DNA test and earlier refusal to address the harm it might have done to their interests, have mostly welcomed her apologies.

And some Democrats in early voting states have seemed unfazed.

Collette Richard, an 18-year-old Des Moines resident and registered Democrat, reacted to the Washington Post story by saying she does not believe the issue should sway voters.

"I mean, your nationality or heritage shouldn't have anything to do with it, it should be your political views and where you stand as an American citizen -- that should pretty much lead you to make your decision," Richard said.

A candidate's ethnicity "doesn't matter," she added.

In Lawrence, the verdict was mostly mixed.

"That's actually one of the reasons why I'm not a huge supporter of her," John Boyle, an 18-year-old Democrat from Andover, said. "I don't love that. I don't think anyone does, so that definitely rubs me the wrong way."

Chrystal Pennisi, 40, who was born and works in Lawrence -- and said she was undecided but liked Warren -- was more forgiving.

"(Warren) was a kid and she was told this is your ancestry, just like any of us were. I don't think any of us really dug into who are parents and grandparents and so on said we were," Pennisi said. "It's not like she stole anything from anyone or she accepted any kind of special award because of it."