If estimates are correct, Kamala Harris drew a bigger crowd at her presidential campaign launch in Oakland than Barack Obama did when he announced his run for president in Illinois in 2007.

Harris, the second African American woman elected to the US senate, has drawn comparisons to Obama since early in her political career. And on Sunday, at least 20,000 people flooded the streets of downtown Oakland to hear the California senator outline her plan for winning the White House in 2020, according to an estimate from local police. Obama’s 2007 campaign launch attracted an estimated 15,000 people.

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Standing in front of seven large American flags, Harris on Sunday afternoon portrayed herself as a fighter, willing to stand up at “an inflection point,” with American democracy under attack “like never before”.

“My whole life, I’ve only had one client: the people,” Harris said, while invoking a career as a prosecutor which started nearly 30 years ago in Oakland.

Play Video 2:46 Senator Kamala Harris announces 2020 presidential bid - video profile

Harris, who was elected to the senate in 2016, announced her run for president last week, on Martin Luther King Jr. Day. She would be both the first African American woman and first south Asian American to be chosen as a presidential nominee. Her campaign logo pays tribute to Shirley Chisholm, the first black woman elected to Congress who in 1972 became the first woman and African American to seek the presidential nomination of a major political party.

Harris’ platform includes Medicare for All, criminal justice reform and the need to respond to the opioid crisis as a public health emergency. “What we don’t need is another war on drugs,” she said. She pledged to act “on science fact, not science fiction” in response to climate change.

Harris assailed Donald Trump’s policies, criticized “the arrogance of power” she saw in wealthy bank executives after the foreclosure crisis, and said that Americans needed to be honest about the country’s problems with racism, sexism, antisemitism and transphobia.

She also emphasized unity, praising “the amazing spirit of the American people” and pledging her desire to be a president, echoing Lincoln: “Of the people, by the people, and for all people.”

“People are trying to convince us that the villain in our American story is each other,” Harris said. “But that is not our story. That is not who we are.”

Facebook Twitter Pinterest Supporters cheer while listening to Kamala Harris speak at the launch of her campaign. Photograph: Elijah Nouvelage/Reuters

“Who are we as Americans?” she asked. Her answer: “We are better than this.”

At one point early in her speech, a heckler repeatedly shouted over Harris. The crowd erupted in cheers and chants of “Ka-ma-la! Ka-ma-la!” until the disruption stopped. “We’ve got you, Kamala,” a man yelled as the cheers died down.

In the hours before her speech, potential Harris voters waited in long lines that snaked up and down multiple Oakland city blocks. Many said that they were only just getting to know the senator’s past and present policy positions, but that it was easy to see the former prosecutor as a formidable opponent to Donald Trump in presidential debates.

Among the tens of thousands who waited in line to hear Harris speak were tech workers and school administrators; doctors from Berkeley and members of Alpha Kappa Alpha, Harris’ sorority; an Oakland high school student preparing to vote for the first time; and an IT worker who had been shaken by the resurgence of racism during Obama’s second term.

Harris “sounds like another version of Obama”, said Mark Olford, 46, who spent more than a decade working in IT in Australia, and said he was troubled on his return to find America seemed to have taken several steps backward on racism.

Electing a candidate of color would help, Olford said, arguing that white political candidates seemed less invested in the struggles of minorities in America.

Bahja Johnson, 29 and a member of Alpha Kappa Alpha, the historic black sorority Harris joined in college, said she would have questions about how well Harris lives up to that campaign slogan: “For the people.” But Johnson also said she wanted to focus for a day on the historic nature of the campaign.

“This is a black woman running for president,” Johnson said, adding that the Harris campaign was tremendously important for women of color even if they do not end up choosing her as their candidate.

“You can’t be it until you see it,” Johnson said her mother had always told her.

Her friend Lauren Zabel, who works in tech, said: “Kamala is an intersectional candidate. She has an Indian mother and a black father. Her husband is Jewish. She’s a stepmother. I think a lot of people can relate to that.”

Both women said Harris’ tough questioning of Trump supreme court nominee Brett Kavanaugh last October made them feel she was representing them in a room of powerful men determined to secure the appointment.

“If she can hold her own there,” Johnson said, “she can hold her own anywhere.”

But both had questions about Harris’ record as a prosecutor, and her choices when as Zabel put it, it came to “putting people of color in jail”.

In a new book, Harris embraces the Black Lives Matter movement and calls for swift action on police brutality. But she is facing scrutiny for the tensions between her progressive rhetoric as a senator and her record as San Francisco district attorney and attorney general of California, particularly on policing, sex work, trans rights and prisons. Activists in San Francisco and Oakland say she ignored calls to use her office to hold police accountable for the killings of black and Latino men.

Johnson on Sunday said she wanted to give Harris a chance to speak to her own record, “before I start to tear apart her platform”.

Taylor Nelson, 17, a high schooler from Oakland, said the rally was her first step in preparing to vote for the first time. Harris’ positions on gun reform, birth control and the border would be important, she said.

“I am happy it’s a lot of women running,” Nelson added.

Senators Kirsten Gillibrand of New York and Elizabeth Warren of Massachusetts and Hawaii congresswoman Tulsi Gabbard have also declared their candidacies.

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There were dissenting voices on Sunday, too. Dina Asfaha, 20, from Berkeley, stood in the street wearing two posters attacking Harris’ record and arguing that Harris was “for the ruling class” and not “for the people”.

Harris “hijacks leftist language language” and “weaponizes her identity”, said Asfaha, who noted she herself was a black woman. A member of the local chapter of Democratic Socialists of America, she said she supported the independent Vermont senator Bernie Sanders for president in 2020.

With her announcement a week ago, Harris joined a crowded Democratic primary field. Michael Bloomberg, the billionaire former Republican mayor of New York City, former vice-president Joe Biden and former Texas congressman Beto O’Rourke are also considering runs, as are senators including Cory Booker of New Jersey, Sherrod Brown of Ohioand Amy Klobuchar of Minnesota. Former housing secretary Julián Castro and South Bend, Indiana mayor Pete Buttigieg have declared campaigns.

Controversy continued on Sunday over the former Starbucks chief executive Howard Schultz’s apparent plan to run as an independent.