Los Angeles (CNN) As Kamala Harris gamely sidestepped questions about her all-but-certain presidential run over the past week, she regaled her audiences with tales of how she -- a woman who was underestimated -- rebuffed the bullying from the big banks after the foreclosure crisis, reminding their legal teams she was "the top lawyer in the biggest state in the country."

She opened up for the first time about the anger she felt as a young girl watching her "brown-skinned" mother followed around a department store. She offered a pre-buttal at every stop to potential criticism from the left that she was part of a system that incarcerated black and brown men, presenting her life's work as that of "progressive prosecutor" who sought to shine a light on injustice.

And in an age when she might end up competing with Beto O'Rourke and his no-holds-barred Instagram account, Harris loosened up a little -- laughing and dancing her way through her playlist for "The Late Show" with Stephen Colbert. There was the song that always makes her dance (A Tribe Called Quest's "Check the Rhime"); the song that reminds her of her college days at Howard University, ("Push It" by Salt-n-Pepa); and her favorite song from childhood (Aretha Franklin's "Young, Gifted and Black").

It was a soft launch for a presidential run that outlined her case to Democratic voters for what makes her unique within a field of presidential candidates, four of whom are likely to be women.

The argument is this: She, as the child of immigrants, who fought her way through the challenges of being a woman of color in politics, to become a prosecutor who would not be bullied, is uniquely positioned to take on President Donald Trump.

In its totality, the tour carried the echo of one of her mother's favorite sayings: "Don't you let anyone tell you who you are. You tell them who you are," as Harris recalled at a book event at LA's Wilshire Ebell Theatre on Sunday.

At a juncture of the presidential race when polls don't mean anything and the depth of each candidate's vulnerabilities is not yet known, Harris is likely to face significant challenges ahead-from her thin experience on foreign policy to the issues that her legal career could pose within a divided Democratic electorate focused on criminal justice reform.

But the composition of each of her audiences this past week -- youthful, racially-diverse and filled with women who view Harris as their champion after her tough questioning of Supreme Court nominee Brett Kavanaugh last year -- underscored the most unique aspect of her potential candidacy: voters of many different races identify with her.

Like Barack Obama before her, Harris seems poised to channel the desire among voters who want to see America's diversity once again reflected in the White House (this time by a woman).

"She is the candidate of where politics will be in 10 years," said 20-year-old Janani Krishnan-Jha, a pre-law junior at Harvard University studying Psychology, South Asian Studies, and Women's Studies who attended Harris' San Francisco event.

Krishnan-Jha noted that her family comes from the same region of India as Harris' mother, giving her special appeal: "There's an untapped pool of voters there. Her being of mixed race represents the increase of diversity in America," she said. "In the social media age, we're listening."

Like Elizabeth Warren -- and now Kirsten Gillibrand, who announced her exploratory committee Tuesday -- Harris is drawing on the electric energy of female Democrats of all races who remain furious with Trump, even after the gains by their party in the 2018 election.

Harris' events also underscore that her prosecutorial turns at the Senate Judiciary Committee grilling Trump nominees and her focus on economic injustice has endeared her to millennials and young voters of color who did not turn out for Hillary Clinton in 2016 at the same level they did for Barack Obama in 2008 and 2012.

At the same time, even as an African American-South Asian woman who became the first black senator from California, interviews and one interruption Saturday night by a heckler in San Francisco suggest that she will have to grapple with criticism within some sectors if the Democratic Party about her record as a prosecutor.

Throughout her career as District Attorney of San Francisco and California's attorney general, some activists felt that Harris should have been more aggressive in driving for changes to the criminal justice system, including bringing more attention to the use of lethal force by police officers.

Death penalty opponents were discouraged by Harris' decision as Attorney General to say while that while she personally opposed the death penalty, she would defend it as a matter of professional duty to her state. (On the flip side, in a controversial 2004 case, Harris took heat when she did not seek the death penalty for the killer of San Francisco police officer Isaac Espinoza).

At the end of her San Francisco event Saturday night, a young woman shouted from the balcony, "What about black people? What about us? What about black people, Kamala!"

San Francisco Mayor London Breed, who was in the midst of wrapping up her discussion with Harris on stage at the Curran Theatre, quieted the heckler by saying, "Excuse me, we're talking," and brought the event to a close.

Asked about the incident, Harris said she was somewhat mystified by the interruption given that she had just spoken at length during the discussion with Breed about racial disparities in healthcare outcomes and her efforts to eradicate racial injustice through her work on criminal justice reform.

"Read the book and look at my life's career," Harris said when asked by CNN how she would have replied to the woman. "Some people have opinions about whether that person was planted. It was toward the end after I had talked about black women and maternal health. I had talked about criminal justice reform, my bill, bail reform, and the disparity in race. So, it was kind of a non-sequitur."

Still, in her new memoir, "The Truths We Hold," Harris addresses the surprise, even within her own family, when she decided to pursue a career as a prosecutor and how she "as a black woman could countenance being part of 'the machine' putting more young men of color behind bars."

She often argues that it is a "false choice" to be placed either in the category of 'tough on crime' or 'soft on crime,' and says she aimed to be "smart on crime" (which was the title of her 2009 book).

Casting herself as a "progressive prosecutor" as she worked her way up from being a line-level prosecutor in Alameda County, to District Attorney of San Francisco, and later California's Attorney General, Harris argues that she sought to be a voice for "the overlooked" to "shine a light on the inequality and unfairness that leads to injustice."

"It is to recognize that not everyone needs punishment, that what many need, quite plainly, is help," Harris wrote of being a "progressive prosecutor."

Even admirers like Los Angeles resident Sandi Cook said it will be important for Harris to keep talking about her record on those issues as she attempts to navigate the Democratic field.

"She does have to address that because it's a really important issue in the black community. It does have to be addressed," said Cook, who attended Harris' LA event late Sunday afternoon. "But I think she was very smart on it, reforming it, and bringing people home who have been in prison for many years for really no reason. She's doing a lot around criminal justice reform, so I think she will address that as she moves forward in 2020."

Throughout the book tour, Harris frequently noted her work with Kentucky Republican Sen. Rand Paul on bail reform and the bill she sponsored with Sens. Cory Booker (D-NJ) and Tim Scott (R-SC) making lynching a federal crime.

She also criticized the divisive history of her own state, and its role in stoking the flames of some of the most high-profile debates over race, ethnicity and civil rights in recent decades.

"There are all these perceptions about who we are as Californians, and it's annoying," Harris said at her event in Los Angeles Sunday evening. She rejected the notion that California is "a state full of progressive people who are aligned with all matters that relate to social justice and civil rights."

"It was California that passed a measure that said undocumented immigrants should not be allowed to have access to public education, public safety and public health," Harris said, referring to Proposition 187, which was struck down by the courts.

"It's the voters of California that passed three strikes, one of the most draconian criminal justice laws in the nation. Because it passed in California, it took hold in other parts of the country. It was the voters of California, in recent history, that passed Prop 8" -- the measure barring same-sex marriages -- "And that is part of our shame."

Most voters are just learning about Harris' background for the first time. In interviews at her events, many Democrats said it is far too early to name their top choices for the Democratic nominee, given how deep and wide the field might be. But they often put her in the category of a fresh generation of leaders-along with other potential contenders like O'Rourke, who lost his bid for Senate in Texas.

"I want some youth and some change," said Mary Beth Reticker, a 62-year-old couples therapist from San Francisco. "The system is so broken.... A younger person might be willing to change things."

Harris new children's book, "Superheroes are Everywhere," has also offered her a chance to connect with an even younger generation of women, including 9-year-old Charlize Patmon, who wrote Harris a letter last year asking her to run for president.

Charlize wrote Harris, her mother said, in part because she sees her own reflection in the California senator.

At Harris' stop at a Los Angeles book store to read her childrens' book, Charlize was just one of many children from multi-racial families who sat on the floor in front of Harris or perched on their parents' shoulders listening to the senator read.

Erica and Dewayne Patmon said they brought Charlize and their other two children because they view Harris' mixed-race heritage as the antidote to Trump and the xenophobic rhetoric he has amplified over the past three years.

Meeting Charlize Sunday, Harris glanced at the letter she had written, in which she encouraged Charlize to keep "challenging conventional wisdom" and said America's future is bright "because of students like you who are passionate about breaking the glass ceiling." "I remember this!" the senator exclaimed.

"Keep doing what you're doing," Harris told Patmon, dancing around the topic of whether she'd run in 2020.

"One day at a time," the senator said Sunday when asked about her current thinking about an announcement. "I'm going to finish this book tour, and then I'll keep moving."