WILMINGTON, Del. (CBS/CNN) — The race to the White House is heating up. Joe Biden and Sen. Kamala Harris made their first public appearance as running mates Wednesday in Wilmington.

Both Biden and Harris criticized President Donald Trump’s leadership, saying this election is a battle for the soul of America.

The duo spoke at A.I. duPont High School near Biden’s home in Wilmington. Several Trump supporters also gathered outside of the school.

“Her story is America’s story. Different from mine in many particulars but also not so different in the essentials,” Biden said of Harris.

It was Harris’ formal introduction after it was announced Tuesday that she would become the first woman of color nominated to seek the office of vice president for a major party — a moment of hope, Biden said, for Black and brown girls.

“Today just maybe they are seeing themselves for the first time in a new way,” Biden said.

The remarks leaned personal.

“Ever since I received Joe’s call, I’ve been thinking yes about the first Biden that I really came to know and that, of course, is Joe’s beloved son — one of his beloved sons, Beau,” Harris said.

Harris’ connection with the Bidens began while she was serving as California’s attorney general.

“The case against Donald Trump and Mike Pence is open and shut,” Harris said.

What Biden and Harris both called their “battle for the soul of the nation” continued with a grassroots fundraiser.

“Our voice is our vote, our vote is our voice,” Harris said.

Supporters who pledged a donation were able to interact and ask questions virtually.

The first-ever virtual Democratic National Convention will kick off on Monday, where Biden and Harris will be formally named as the party’s nominees.

Harris laid out the Democratic case against President Trump in her first speech as Biden’s running mate Wednesday, arguing that Trump isn’t “up to the job.”

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In the speech, Harris sharply criticized Trump’s handling of the coronavirus pandemic, comparing the lives lost to Ebola, in which two Americans died, during former President Barack Obama and Biden’s administration. She also lambasted Trump’s handling of the economic fallout caused by the crisis.

“He inherited the longest economic expansion in history from Barack Obama and Joe Biden. And then, like everything else he inherited, he ran it straight into the ground,” she said of Trump.

“This is what happens when we elect a guy who just isn’t up for the job,” Harris said. “Our country ends in tatters and so does our reputation around the world.”

The two speeches — first Biden, then Harris — served as introductions to the new Democratic ticket. But they also offered a preview of how Biden, Harris and their surrogates will attack Trump and Vice President Mike Pence’s time in office during next week’s virtual Democratic National Convention and in the sprint to November’s general election that follows.

Before introducing Harris, Biden said the election poses moral questions that Americans must answer.

“Who are we as a nation?” Biden said. “What do we stand for? And most importantly, what do we want to be?”

In his speech, Biden said he’d first learned about Harris through her relationship with Beau Biden, who died of brain cancer in 2015.

“Kamala, you’ve been an honorary Biden for quite some time,” he said as he introduced Harris.

Harris said that during the Great Recession, she as California attorney general and Beau Biden as Delaware attorney general spoke on the phone daily — sometimes multiple times per day.

“I learned quickly that Beau was the kind of guy who inspires people to be a better version of themselves. He really was the best of us. And I would ask him, where’d you get that, where’d this come from, he’d always talk about his dad,” she said. “The love that they shared was incredible to watch. It was the most beautiful display between a father and a son.”

Their comments underscored that both candidates — publicly, at least — have put behind them Harris’ attack on Biden over his record on busing to desegregate schools in a June 2019 Democratic presidential debate.

Biden said that with Harris now on the Democratic ticket, “Little Black and brown girls, who so often feel overlooked and undervalued in their communities, but today, just maybe they’re seeing themselves for the first time in a new way.”

Biden began his speech in Wilmington by thanking other women his campaign vetted for the vice presidential pick, before he chose Harris — the daughter of Indian and Jamaican immigrants — on Tuesday.

“As a child of immigrants, she knows personally how immigrant families enrich our country,” he said. “Her story is America’s story.”

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Biden also lambasted Trump for immediately referring Tuesday to Harris as “nasty,” a term Trump has directed at other women in the past.

“Is anyone surprised Donald Trump has a problem with a strong woman, or strong women across the board?” Biden said.

He added: “Kamala Harris has had your back and now, we have to have her back. She’s going to stand with me in this campaign, and all of us are going to stand up for her.”

Wednesday was the first day Biden and Harris campaigned together in person. After Biden offered Harris the vice presidential spot on the Democratic ticket on Tuesday, Harris traveled to Delaware on Wednesday. Biden, Harris and their spouses Jill Biden and Doug Emhoff met at Biden’s house before the speech, and were seen leaving for the venue in Wilmington in separate SUVs.

Biden joked that Emhoff, too, would have to adjust to his historic status as — if Biden and Harris win — “America’s first second gentleman.”

It’s not yet clear whether they’ll be able to continue to campaign together, with the coronavirus pandemic limiting Biden’s ability to hold events since mid-March.

Next week’s Democratic National Convention would ordinarily kick off a frenetic two-and-a-half month sprint to the November 3 election, but the pandemic has limited Biden to socially distanced events with small crowds. He spent July delivering weekly speeches detailing planks of his economic agenda.

After the speech, Biden and Harris are set to appear together at an online fundraiser for “grassroots” small-dollar donors on Wednesday night.

Asked by CNN if the two would campaign together, Biden said after their speeches Wednesday that “if the science allows us, you’re gonna see us campaigning together.”

CBS3’s Joe Holden and Alexandria Hoff contributed to this report.

(©Copyright 2020 CBS Broadcasting Inc. All Rights Reserved.The-CNN-Wire™ & © 2020 Cable News Network, Inc., a Time Warner Company contributed to this report.)