Donald Trump and Kamala Harris closed out the tumultuous 2024 campaign with competing rallies across Pennsylvania, offering contrasting visions – and moods – in the final hours before polls opened in an election both candidates have cast as an existential fight for America’s future.

In Philadelphia, Harris ended a frenetic dash across the state at the art museum steps made famous in the film Rocky – “a tribute to those who start out the underdog and climb to victory” – where tens of thousands of supporters gathered for the star-studded event.

“Momentum is on our side,” Harris declared to roars from the crowd.

Earlier in the day, Harris rallied in Allentown, Scranton and Pittsburgh. She also made stops in Reading to visit a Puerto Rican restaurant with congresswoman Alexandria Ocasio-Cortez and to join a canvas for her own presidential campaign. “I wanted to go door-knocking!” Harris told the family, stunned to see the vice-president on their porch.

Trump, by contrast, appeared hoarse and exhausted at times, as barnstormed the battleground states, holding rallies in Raleigh, North Carolina, two in Pennsylvania and a late-evening event in Grand Rapids, Michigan – where he ended his two previous presidential campaigns. His remarks were dark and dystopian, rife with warnings that cast migrants as dangerous criminals and personal attacks on a number of high-profile Democratic women. He has continued to boast about his crowd sizes, but reports suggest some of his final events have been plagued by empty seats and early departures from audience members during his lengthy, meandering speeches.

“Tonight, then, we finish, as we started, with optimism with energy, with joy,” said Harris, who was introduced by Oprah Winfrey in Philadelphia. Behind her, the steps were illuminated blue and a large “President for All” banner was displayed. It all matched the mood of Harris’s positive closing argument, an attempt to shift the focus away from the threat posed by the ex-president, whom she did not mention by name in her remarks or her final ad.

Lady Gaga and Ricky Martin performed at the event, while Oprah Winfrey brought on-stage 10 first time voters to share their reason for supporting Harris. Winfrey perhaps provided the starkest warning of the night, suggesting a second Trump presidency be the end of free and fair elections in the United States.

“If we don’t show up tomorrow, it is entirely possible that we will not have the opportunity to ever cast a ballot again.”

As the Harris campaign and its surrogates have continued to appeal to female voters, Trump revived familiar insults against notable women, sometimes with violent language.

In North Carolina, he attacked former first lady Michelle Obama, saying: “She hit me the other day. I was going to say to my people, am I allowed to hit her now? They said, take it easy, sir.” He also suggested the Democratic congresswoman Nancy Pelosi should have been jailed for ripping up a copy of his 2020 State of the Union address: “She’s a bad, sick woman, she’s crazy as a bedbug.”

And Trump repeated his line that Harris is a “low IQ individual”, followed by an incoherent tangent seemingly imagining her struggling to sleep: “I don’t want to have her say, You know, I had an idea last night while I was sleeping, turning, tossing, sweating,” he said, without finishing the sentence.

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Trump leaned into his taunts as he continues to face scrutiny over his recent comment suggesting that Liz Cheney, the former GOP congresswoman and a Harris supporter, should face rifles “shooting at her”. Appearing on ABC’s The View on Monday, Cheney said, “Women are going to save the day” on Tuesday.

In North Carolina, Trump also threatened the newly elected president of Mexico, Claudia Sheinbaum, suggesting he would impose tariffs on all Mexican goods “if they don’t stop this onslaught of criminals and drugs” – part of his trade proposals that economists have warned could significantly raise costs for US consumers.

At around the same time, Harris was rallying in Allentown, roughly 40 miles away, critiquing Trumpism without directly naming her opponent: “America is ready for a new way forward, where we see our fellow American not as an enemy but as a neighbour. We are ready for a president who understands that the true measure of the strength of the leader is not based on who you beat down. It is based on who you lift up.”

Later, Trump’s running mate, JD Vance, earned loud applause at a rally in Georgia, when he attacked Harris by bringing up Joe Biden’s recent gaffe, in which he appeared to call Trump supporters “garbage”.

“In two days, we are going to take out the trash in Washington DC, and the trash is named is Kamala Harris,” said the Ohio senator, in a remark that was condemned by Democrats and pundits.

The back-and-forth trash talking originated with a comedian’s racist joke at Trump’s recent New York rally, calling Puerto Rico a “floating island of garbage”, a comment that many Harris surrogates cited on Monday while appealing to Puerto Rican voters in Pennsylvania.

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By his evening rally in Pittsburgh, Trump returned to his crowd size obsession, making false claims about low turnout at Harris’s nearby rally that hadn’t yet begun. He then mocked Beyoncé, who rallied for Harris in Texas: “Everyone’s expecting a couple songs and there were no songs. There was no happiness.” He added, “We don’t need a star. I never had a star.”

The final scramble to turn out voters comes as Trump continues to make false claims about voter fraud, raising fears about how he might challenge the results if Harris wins. In a call with reporters on Monday, the Harris campaign said it was prepared to combat any efforts by Trump to discredit the outcome.

“We have hundreds of lawyers across the country ready to protect election results against any challenge that Trump might bring,” said Dana Remus, a senior campaign adviser and outside counsel. “This will not be the fastest process, but the law and the facts are on our side.”

Legal challenges were designed to undermine faith in the electoral process, she added: “Keep in mind that the volume of cases does not equate to a volume of legitimate concerns. In fact, it just shows how desperate they’re becoming.”

There are also growing fears that political violence will escalate on election day and beyond, as misinformation and conspiracy theories are expected to spread while counting is under way. Election officials in one Nevada county said on Monday that threats have become so severe that polling places have installed “panic buttons” to automatically call 911 in emergencies.

At Trump’s Pittsburgh rally, Michael Barringer, a 55-year-old coalminer, expressed his disdain for undocumented immigrants in explaining his support for Trump: “You’ve got millions and millions of illegal aliens crossing the border. They don’t speak English. They don’t say a pledge allegiance to the flag. They freeload off of us. I’m all for legal immigration, but not coming across the border illegally, taking American jobs.”

Elizabeth Slaby, 81, was the first in line at Harris’s Allentown rally, arriving at about 6am. She said she was a registered Republican for more than 50 years, but changed her registration after the January 6 attack: “I never thought I’d see a woman president and now I’m so, so excited.”

Sam Levine Smith contributed reporting

Read more of the Guardian’s 2024 US election coverage:

• US election 2024 live updates: latest polls, results and news

• When do polls close?

• How the electoral college works

• Where is abortion on the ballot?

• Senate and House races to watch

• Lessons from the key swing states

• Trump v Harris on key issues

• What’s at stake in this election

• What to know about the US election

• US elections 2024
• Kamala Harris
• Donald Trump
• US politics
• Democrats