Donald Trump All But Assured White House Victory After Claiming Pennsylvania – but Clinton Won't Concede Tonight

Donald Trump and his family have “started celebrating” as the GOP nominee won the battleground states of Pennsylvania, Florida, Ohio and North Carolina – but Hillary Clinton isn’t giving up yet.

The victory in Pennsylvania, which has gone for the Democratic candidate every year since 1988, seemed a mortal blow for Clinton’s chances at the presidency, according to many Electoral College experts.

Hillary for America campaign chairman John Podesta took the stage at Javits Center at 2 a.m. on Nov. 9, telling supporters, “Well folks, I know you’ve been here a long time and it’s been a long night and it’s been a long campaign, but I can say, we can wait a little longer can’t we?”

Sending those gathered at the Manhattan rally home, Podesta said, “We’re not gonna have anything more to say tonight.”

“Everybody should head home, you should get some sleep,” Podesta advised. “Your voices and your enthusiasm means so much to her and to Tim and to all of us. We are so proud of you. We are so proud of her. She’s done an amazing job and she is not done yet.”

He added, “So thank you for being with her, she has always been with you. Goodnight. We will be back. We’ll have more to say. Let’s get those votes counted and we’ll bring this home.”

Races in New Hampshire, Arizona, Minnesota, Wisconsin and Michigan were still tight ahead of Podesta’s speech.

A source close to the Trump family tells PEOPLE that “the Trumps are frustrated by the delay and by Hillary’s decision to basically go to bed tonight without waiting on the final results, but they know it’s only a matter of time.”

Veteran Republican campaign adviser Lou Midkiff, who works closely with Trump’s vice presidential running mate, Indiana Gov. Mike Pence, told PEOPLE the Pence campaign has “been very confident in this win. The enthusiasm you see on the road is palpable … You can cut it with a knife.”

“It’s only been two weeks since Hillary [Clinton] was leading in the polls, but he closed the gap and turned it around,” Midkiff continued. “For the last seven days, everyone inside the Pence campaign has been very confident in a win. We knew we would get Ohio. Florida is ours. North Carolina is a wonderful surprise. Trump is a rock star when you deal with him. He can talk to anybody. And Pence is the same.”

Midkiff added that Pence campaign events have seen surprisingly high turnouts.

“The Pence campaign would have judged a successful event by a few hundred people turning up … With a vice president, that’s all you expect,” he said. “But thousands of people would come and not everyone could even get in — they didn’t fit in the venues. It was so obvious this was a bigger deal than anyone thought.”

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Supporters were jumping up and down at the party for Trump in New York after North Carolina was called for the candidate. Later, as the electoral votes racked up, people at Trump’s event were screaming, chanting “USA USA” and singing “God Bless America.”

They also began chanting “lock her up” in regards to Hillary Clinton.

As Trump’s lead grew, the number of people crowding into the ballroom of the Hilton Hotel in Midtown Manhattan increased over-capacity. The space became so claustrophobic, one woman fainted.

And as the results stopped rolling in and more than an hour went by without any new announcements, supporters who had been dancing, singing and shouting grew restless. People began crowding in and staring at the TV screens, waiting with bated breath for the Michigan win people are saying is inevitable.

As of 2:20 a.m. ET, Trump had projected wins in 26 states, giving him 267 electoral votes.

A source told PEOPLE Tuesday night that “Trump and his kids are feeling very good right now.”

The GOP nominee’s daughter Ivanka took to Instagram shortly after 9 p.m. ET to share a photo of the whole family, along with Trump’s running mate Mike Pence, watching the election results come in from Trump Tower.

“Watching the votes come in at HQ #election2016 #MAGA,” she captioned the snap.

Trump shared a similar family photo on his Twitter, captioning it, “Watching the returns at 9:45pm. #ElectionNight #MAGA.”

Meanwhile, at Clinton’s election night event at the Javits Center in N.Y.C., a source told PEOPLE the mood was “swinging.”

There were long silences on the floor as TV screens showed states turning red or being declared too close to call. There were huge cheers at one point when Clinton was projected to win New Mexico.

Speaking to PEOPLE while her own swing state was still up in the air, Florida Congresswoman Debbie Wasserman Schultz said she remained “hopeful” that Clinton would win the night.

“I’m a little nervous,” the former Democratic National Committee chair told PEOPLE. “I expected to be nervous — it was going to be a close election, we’re a pretty divided country.”

Wasserman Schultz said she’s been “on phone nonstop” checking in with people back in Florida.

“We’ve got about 93 percent of the state reported, but my county, which has the largest number of Democratic, is only about 50 percent in,” she said at the time. “So a huge Democratic caucus left to report.”

Wasserman Schultz, who easily won re-election in South Florida’s congressional district on Tuesday, resigned as chair of the DNC in July after hacked emails suggested that DNC staffers conspired against Clinton’s primary rival Bernie Sanders.

Trump’s family was feeling uneasy earlier in the evening, two sources close to family members told PEOPLE.

A third insider added, “It’s been very tense behind the scenes among the family members. Everybody is on edge. They honestly feel that it could go either way.”

Outside his headquarters, the GOP nominee’s supporters gathered and chanted “Drain the swamp” and “Lock up Hillary” as polls on the East coast of the country closed Tuesday evening.

Earlier in the day, the 70-year-old Republican candidate’s children and grandchildren headed to the polls to cast their votes in New York City. Ivanka brought 5-year-old daughter Arabella — who sported an “I Voted” sticker after her mother went into the booth — along for the experience, while Donald Jr. brought four of his five children with wife Vanessa.

The GOP nominee was caught peeking over his wife’s voting box at P.S. 59 in N.Y.C. Tuesday morning, seemingly checking to confirm that he did, in fact, earn her support. His son Eric Trump was also photographed peeking at his wife Lara Yunaska’s ballot as she voted.