A sea of pink hats – the symbol adopted by many attendees – flooded past workers taking down the grandstands for Trump’s inauguration and parade on Friday. Subway stations across the DC area were so clogged that operators recommended walking miles into town. Similar turnouts totaling several million nationwide appeared in major cities from Boston to Chicago to Los Angeles.

“This is the moment of the beginning of the revival of the women’s movement,” Senator Kirsten Gillibrand of New York declared to the crowd here.

But is it? Despite the turnout, questions remain. Will protesters unified against Trump in the wake of a divisive campaign stay together or splinter? Will the already unpopular president change in any substantial way as a result of protests or dig in? And will protests accrue to his benefit or detriment among Americans who have not already picked a side in the fight?

Watch: Donald Trump is sworn in as US president

Talk of how to sustain momentum against Trump reverberated through the crowds, as marchers spoke of trying to form a lasting opposition.

“I will help sustain it because he stands against everything America is for, in my opinion,” said Sheila Thunboe, 63, who travelled to the Washington march from her home in Denver, en route to business meetings in Miami.

It was her first protest, Thunboe said, since she’d marched against the Vietnam war while a college student.

The gatherings across the country reflected in some ways the divided presidential vote, with huge crowds in urban centres that went to Hillary Clinton and smaller events in areas dominated by Trump. Collectively, however, they posed an immense public relations problem for the new president, who already was coming into office with record low approval ratings.

His day was spent in part trying to smooth over another dispute, travelling to the CIA mid-afternoon to express his support for the agency. His appearance followed weeks of squabbling with intelligence agencies about their determination that Russia had worked to defeat Clinton with a disinformation and hacking campaign.

Trump had no immediate response to the day’s protests, a departure from his usual practice, although he did indulge in a lengthy attack on the news media for reporting that the size of the crowd at his inauguration had been smaller than the audience for Barack Obama’s swearing-in.

He later tweeted criticism of the protests, while pointing to the TV ratings for his inauguration: “Watched protests yesterday but was under the impression that we just had an election! Why didn’t these people vote? Celebs hurt cause badly.

“Wow, television ratings just out: 31 million people watched the Inauguration, 11 million more than the very good ratings from 4 years ago!”

Trump has in the past proved exceptionally sensitive to the public’s perception of him. In almost every campaign event, he either boasted about his standing in polls – if he was winning – or, if not, lacerated pollsters.

He has also continuously claimed, wrongly, that the news media never reported his sizeable campaign crowds. Recently, he took to Twitter to mock Arnold Schwarzenegger for not getting the high ratings he had received on NBC’s Celebrity Apprentice.

“He’s a narcissist, and he seems to hopefully care what other people think of him,” said Lisa Ellern-Feldman of Chevy Chase, Maryland, who was pushing a stroller on a long walk to the Washington protest site. “I don’t know. Let’s hope.”

But the task ahead of protesters is potentially more difficult – maintaining unity despite the disparate issues and ideologies that brought the crowds together on Saturday.

The protests replicated one of the problems that limited Clinton’s appeal in November: many people disapproved of Trump but without a well-honed reason to vote for Clinton they lost interest in the election.

Protesters mentioned a range of reasons for their attendance, from Trump’s cabinet picks to his campaign rhetoric to his intentions regarding funding of the arts. Republican plans to defund Planned Parenthood and repeal the Affordable Care Act, or Obamacare, were huge draws.

“People were brought together mostly by their opposition to him,” said Patrick Egan, an NYU political scientist. “But it was not like rallies for reproductive rights or gay rights. Often without unifying issues, it is difficult to sustain that unity.”

Recent history has demonstrated the alternatives for protest groups. The conservative tea party movement rose in opposition to then-president Obama and his health care and economic stimulus plans. By filling congressional town halls with their protests, they helped to fuel unified Republican opposition to the president – and pushed their own party in a more conservative direction.

The Occupy Wall Street protesters, on the other hand, failed to turn their organisation into that kind of powerhouse and ended up in a niche ignored by both parties.

They also proved a truth about protests: the ones that come to represent extremes rarely manage to benefit their cause and instead empower their opponents. Violent protests against Trump during the campaign often solidified support for him among voters who disagreed with the tactics of the opposition and saw him as a victim.

The party with the most to gain from the protests also faces its own difficulties. Democrats have been casting about for a direction ever since the primary battle between Clinton and Senator Bernie Sanders of Vermont.

For all the spirit showed by the protesters, the day was filled with reminders of splits that have yet to be repaired.

Clinton, who never inspired the sort of passion that powered Saturday’s rallies, tweeted her support for the marchers.

“Thanks for standing, speaking & marching for our values,” she wrote, and then invoked her campaign slogan. “I truly believe we’re always Stronger Together.”

Congresswoman Debbie Wasserman Schultz of Florida, blamed by some in her party for opposing Sanders while she was a supposedly neutral Democratic National Committee chair, spoke from the Washington stage.

So did filmmaker Michael Moore, whose statements effectively sought to impugn both of them.

“The old guard of the Democratic party has to go,” said Moore, who endorsed Sanders during the primaries. “We need new leadership.”