(CNN)President-elect Joe Biden addressed a deeply divided nation Saturday night, turning to the challenges ahead by grounding his victory speech in the spirit of compromise, asking supporters of President Donald Trump to give him a chance, and calling on all Americans to turn the page from what he described as a “grim era of demonization.”Biden made that plea for unity and understanding in his home town of Wilmington, Delaware, at an extraordinary moment in American history when the current occupant of the White House showed no indication that he plans to concede to his rival and continued to push the fiction on Twitter that he had won the election, while making baseless accusations about how the election was stolen from him.After jogging on stage wearing a mask, Biden repeated his promise that he would seek to unify rather than divide. He pledged to govern by the creed that he does not see blue states and red states, but only the United States.When the campaign started nearly two years ago, it would have been extraordinary to think that Americans would show up to a victory rally wearing masks. The fact that they had to, and at a drive-in event outside in November, was a reminder of the moment of national extremist that Biden and Harris will inherit in January.

She also credited Biden for having the “audacity to break one of the most substantial barriers that exists in our country and select a woman as his vice president.””While I may be the first woman in this office, I will not be the last, because every little girl watching tonight sees that this is a country of possibilities.””And to the children of our country, regardless of your gender, our country has sent you a clear message: Dream with ambition, lead with conviction, and see yourself in a way that others might not see you, simply because they’ve never seen it before. And we will applaud you every step of the way.”As Biden and Harris prepared for those victory speeches, jubilant celebrations erupted in big cities across America, with supporters pouring into the streets — shouting, chanting, singing, dancing and waving flags as drivers honked their horns — to mark the victory and the end of Trump’s presidency.The celebrations began near the White House on Saturday while Trump was golfing in Virginia — forcing the smoldering President to wind his way back to 1600 Pennsylvania Avenue in his motorcade through those crowds after hitting the links. There was no sign that Trump would extend the traditional invitation for a White House visit to the President-elect as he continues to falsely maintain that the election was stolen from him.

Trump’s refusal to concede

While Trump has yet to give any public sign he’s prepared to relinquish power, Jared Kushner, the President’s son-in-law and senior adviser, has approached him about conceding the election, two sources tell CNN Saturday.Trump has not denied the outcome of the election, privately at least, sources tell CNN. But he’s continuing to push his attorneys to pursue legal challenges that would delay formal certification of the results. Chief of staff Mark Meadows, who is working from home after testing positive for coronavirus, discussed next steps with the legal team Saturday.Trump again on Saturday baselessly impugned mail-in ballots, which overwhelmingly tipped the election in Biden’s favor, and repeated the falsehoods on Twitter that he “WON THE ELECTION.” He claimed “bad things happened” in the election that his poll observers were not allowed to see, even though there is no evidence that GOP poll watchers were systematically shut out of the process anywhere in the country.”71,000,000 Legal Votes. The most EVER for a sitting President!” Trump tweeted Saturday afternoon. (While the popular vote tally was continuing to rise for both men as ballots were counted Saturday, Biden had won 74.5 million votes and Trump had won 70.4 million votes).Trump’s campaign team is expected to continue its effort to dispute the election results with a next round of lawsuits Monday, but so far they have been unable to point to any credible instance of voter fraud that would alter the outcome of the race.

It is not clear how isolated instances of irregularities, even if found, would add up to a case with sufficient legal questions to make it all the way to the Supreme Court or would challenge the integrity of an election that Biden looks set to eventually win with sufficient electoral votes, which would make challenges in individual states unlikely to alter the national result.The legal front looks increasingly like a rallying point for partisans keen to prevent Biden’s presidency from being seen as legitimate by Trump supporters and as a face-saving way for the President himself to explain his defeat. Renowned Republican election lawyer Benjamin Ginsberg said that there was no sign that the President had any case that could change the result of the election. He told CNN’s Erin Burnett that there was so far “no evidence of the systemic fraud or irregularities to cast any of the results in any of the states into doubt.”The White House signaled that the public was unlikely to see the President soon after he returned from playing golf Saturday afternoon, but he was well within earshot of the crowds clamoring for his exit in Washington, DC.One joyful gathering was directly across from the White House in Black Lives Matter Plaza, near where the Trump administration enraged activists in June by clearing peaceful protesters with pepper balls, flashbangs and rubber bullets during a demonstration against police brutality shortly before Trump walked across the street for a photo op while holding a Bible in front of historic St. John’s Church.While Trump may not accept that he has lost, many world leaders did on Saturday as they sent congratulatory messages to Biden and Harris.In a sign of how quickly global realities shift after a US election, even some leaders who had courted Trump, including British Prime Minister Boris Johnson, rushed to congratulate the President-elect.In perhaps the most notable message, India’s nationalist Prime Minister Narendra Modi, who had appeared at huge campaign-style rallies with Trump in India and the United States, tweeted a picture of Biden leaning in to whisper in his ear during a previous meeting. Modi sent a separate tweet congratulating Harris and noting her Indian heritage, saying her success was a great source of pride for Indian Americans and her “chittis” — a Tamil term of endearment that has been used by the vice president-elect.

A complex governing challenge ahead

Many prominent Republicans remained silent on Saturday, but there were a few exceptions, including former Florida Gov. Jeb Bush — who lost the nomination to Trump in 2016 — and Utah Sen. Mitt Romney, the 2012 Republican nominee. Trump’s failure to concede and congratulate his opponent may have suppressed normal courtesies from Republican leaders who remain intimidated by him and dependent on the President’s base for their reelection prospects in 2024.Though Biden pulled off an impressive feat by dispatching an incumbent president and rebuilding the Democrats’ “blue wall” in the Midwest, he is keenly aware of the enormous governing challenge facing him given his slender margin of victory in key swing states. Beyond that — despite fervent hopes that they could deliver a sharp repudiation of Trump and his party at the polls — Democrats actually lost seats in the US House, though they will maintain a majority. Despite massive fundraising, Democrats also failed to make much of a dent in the GOP-controlled Senate. The balance of power in the chamber hinges on two likely runoff elections in Georgia in January.Biden outlined ambitious goals during his campaign — from a major revamp of the tax code to aggressive efforts to deal with the climate crisis to an expansion of Obamacare — as he tried to hold his fractious party together and inspire the loyalty of progressive Democrats who backed Vermont Sen. Bernie Sanders.The pressures from the left were already apparent on Saturday. “I think he has a really, really strong mandate,” Sanders told CNN’s Anderson Cooper. “Now it’s time for working people to be heard and for their pain to be addressed.”But the political reality of a still-polarized nation, a divided government in Washington and the difficulty of solving the nation’s Covid-19 crisis are likely to temper Biden’s ambitions.In his remarks Saturday night, Biden promised to get the pandemic “under control” so Americans could reclaim their most precious moments — from visiting with their grandchildren to celebrating weddings and graduations. He noted that he would name a group of leading scientists and experts to his coronavirus task force on Monday, who would build an “action blueprint” that could be deployed as soon as he is inaugurated in January.The task force will be headed by three co-chairs: former Surgeon General Vivek Murthy, former Food and Drug Administration Commissioner David Kessler and Dr. Marcella Nunez-Smith, an associate professor of medicine and epidemiology at Yale University’s School of Medicine, CNN reported Saturday.Biden’s plan to tackle the virus, he said, would be rooted in science and constructed out of compassion, empathy and concern.As he did throughout the campaign, Biden spoke to the grief that many Americans have experienced during the pandemic, alluding to the loss of his own son Beau Biden, the former attorney general of Delaware who died of brain cancer at the age of 46.Capturing the faith that sustains him, Biden quoted from a Catholic hymn — “On Eagle’s Wings” — that he said had meant a great deal to his family and to Beau Biden.”I hope it can provide some comfort and solace to the 230,000 Americans who have lost a loved one to this terrible virus this year. My heart goes out to each and every one of you,” Biden said.As CNN’s Arlette Saenz reported, there was another reminder of Beau as fireworks lit up the sky outside the Chase Center: One of the songs that played during the show was “A Sky Full of Stars” by Coldplay, one of Beau Biden’s favorite bands.Former President Barack Obama underscored the challenges ahead for his former vice president on Saturday when he asked Americans to set aside their political differences and “give him a chance and lend him your support.””When he walks into the White House in January, he’ll face a series of extraordinary challenges no incoming President ever has — a raging pandemic, an unequal economy and justice system, a democracy at risk, and a climate in peril,” Obama said in a statement. “I know he’ll do the job with the best interests of every American at heart, whether or not he had their vote.”Obama noted that the election results “at every level show that the country remains deeply and bitterly divided.””It will be up to not just Joe and Kamala, but each of us, to do our part — to reach out beyond our comfort zone, to listen to others, to lower the temperature and find some common ground from which to move forward.”