Atlanta (CNN) In the aftermath of last year's election, the centrist old guard is out and progressives have won the battle for the soul of the Democratic Party, Elizabeth Warren declared Saturday.

"But, boy, we've inherited a hell of a challenge, haven't we?" she said at an annual gathering here of thousands of progressive activists.

In a speech that outlined Warren's vision for the party's future, the Massachusetts senator offered a series of policy prescriptions, calling on Democrats to push for Medicare for all, debt-free college or technical school, universal pre-kindergarten, a $15-an-hour minimum wage and portable benefits.

She dug in against President Donald Trump, saying Democrats would defend undocumented immigrants brought into the United States as children and that "we're never, ever going to build your stupid wall."

And she celebrated the ascendant progressive wing's takeover of the party -- which has accelerated since November's election.

"We don't have to tip-toe anymore. We don't have to hedge our bets," Warren said.

Through her speech, Warren didn't shy away from the prospect of a 2020 campaign for the presidency.

"We're going to fight to put more women in positions of power," she said at one point, "from committee rooms to boardrooms to that really nice oval-shaped room at 1600 Pennsylvania Avenue."

The crowd responded with chants of "Warren 2020!" Warren paused and smiled, and then moved on without directly addressing the chants.

Warren is already seen as one of Democrats' foremost voices -- along with Vermont independent Sen. Bernie Sanders -- on progressives' economic policies.

So she used her speech in front of about 3,000 attendees at the progressive Netroots Nation conference Saturday to dive into issues of culture, which have split progressive and centrist Democrats since Hillary Clinton's loss in November.

In a shot at Bill Clinton-era Democratic policies, Warren said Democrats are not "going back to the days of welfare reform and the crime bill."

"We're not going back to the days of being lukewarm on choice," she said. "We're not going back to the days when universal health care was something Democrats talked about on the campaign trail but were too chicken to fight for after they got elected."

Warren's comments came at a crucial moment for the Democratic Party.

Its base is energized by the fight against Trump, and Democrats were thrilled to see the GOP effort to repeal former President Barack Obama's Affordable Care Act fail in late July.

However, the party is also without a national leader, and its path forward on policy is not yet settled.

For the first time in decades, Democrats reacted to a national election loss by moving leftward -- rather than to the center. The party's leaders have embraced confrontational tactics against Trump, while a growing list of its top prospects for the 2020 presidential race -- including Warren -- are embracing Sanders' call for a "Medicare for all" single-payer health care system.

But that shift has caused consternation in some quarters. Some leading Democrats -- including Colorado Gov. John Hickenlooper, New Orleans Mayor Mitch Landrieu and Florida Rep. Stephanie Murphy -- recently backed the launch of a group called "New Democracy," aimed at moving Democrats toward positions that can win over moderates, independents and disaffected Republicans.

Warren pointed to a New York Times op-ed by Mark Penn, a Hillary Clinton 2008 campaign strategist, who called for the party to abandon "identity politics."

Warren noted that those calls, after previous election losses, had prevailed.

"This time, no one cared," she said. "Big yawn."

"In the wake of the last election, I've heard people say we need to decide whether we're the party of the white working class or the party of Black Lives Matter," Warren said.

"I say we can care about a dad who's worried that his kid will have to move away from their factory town to find good work -- and we can care about a mom who's worried that her kid will get shot during a traffic stop," she said. "The way I see it, those two parents have something deep down in common -- the system is rigged against both of them -- and against their kids."

Warren argued that many of the voters who abandoned Democrats and either fell into Trump's camp or stayed home in November because they see a "rigged" system and "don't feel like anyone in politics is doing anything to un-rig it, or it's too broken to un-rig at all."

"So spare me the argument about whether we ought to be trying to bring back folks who voted for Donald Trump or trying to turn out folks who just didn't vote," she said. "Because we can't do either of those things until we can show that things can change -- and that we will fight to change them."

Warren broke out her biggest applause line mid-speech, saying Democrats don't need permission from Senate Majority Leader Mitch McConnell -- a reference to a clash between her and the Kentucky Republican earlier this year.

"He would probably tell me to sit down and shut up," Warren said. "Nevertheless, I would persist."