Image copyright Getty Images Image caption Donald Trump's arrival in Florida in stormy conditions provided plenty of drama

Donald Trump spent the day after the Big Debate claiming - in tweets, press releases and interviews - that he won the showdown with Hillary Clinton.

Some of his supporters here in Melbourne, Florida, weren't so sure, but they came to his Tuesday night rally by the thousands anyway, to shower their candidate with love and adulation.

"I've never seen anything like this before," Pat Miller, a retiree who has lived in Melbourne for 50 years, said of the massive turnout for the campaign event in the usually sleepy coastal town.

She added that she was hoping to get "our Trump back" after what she said was his less than aggressive performance in the debate. "I think he needs to hit her harder."

She wasn't alone.

Image caption Janusz Biskupek had some advice for Mr Trump

Janusz Biskupek, a Polish immigrant from Boca Raton who works in a window and door factory, said Mr Trump should fire his debate advisers.

"I don't kiss asses," said Mr Biskupek, dressed in a white racing outfit with "Donald you are the future" printed on it. "I didn't like the debate, and I want him to be more prepared next time. Mr Trump is very smart, but he doesn't have experience in politics."

The queue for Tuesday night's rally at a local airport hangar snaked out across a wide parking lot, to a nearby road and back again.

The crowd of 7,500 - with thousands more held outside by the fire marshal - cheered when the Trump-emblazoned aeroplane taxied to the hangar, as the soundtrack to the action film Air Force One blared over loudspeakers. Lightning struck from dark clouds in the distance, setting the scene for a grand theatrical entrance.

They went into a frenzy when the door opened and Mr Trump emerged.

And they chanted and waved their signs as Mr Trump took to the stage and boasted that the polls (albeit online and very unscientific) showed he had prevailed against his Democratic opponent.

Media playback is unsupported on your device Media caption Some supporters of Donald Trump seemed disappointed by his performance in the first debate against Hillary Clinton and are calling for a more aggressive approach.

Despite his assurances that he had soundly beaten "crooked Hillary Clinton" (and more traditional measures showed her with the upper hand), for most of the evening Mr Trump seemed determined to re-litigate the previous night's encounter with the former secretary of state.

"She bragged about how she travelled all of the world," he said. "And you know what it got us? Nothing. It got us death and got us debt."

Earlier in the day he told a town hall forum that he might "hit Hillary harder" next time, and on Tuesday night he said that he had been "holding back" during the debate - perhaps another veiled reference to a decision not to criticise President Bill Clinton's marital infidelities.

He said, however, that he had been watching the former secretary of state "very carefully".

"For 90 minutes on issue after issue, Hillary Clinton defended the terrible status quo," he said. "We have to have dramatic change."

It was a point that he had tried to emphasise on Monday night, and he returned to it several times at his rally.

He said Mrs Clinton had backed disastrous trade deals like the North American Free Trade Agreement. Iraq and Libya are in chaos of her making, he continued. And American allies must pay more for the cost of their national defence.

Image copyright Getty Images

Although Mr Trump relentlessly bashed his Democratic opponent, he reserved some of his sharpest barbs for the "dishonest" national media - which, in the hours after the debate, had largely passed a negative verdict on his performance.

Time and time again on Tuesday evening, he lobbed insults their way, as the crowd jeered and cursed.

The only weapon Mrs Clinton has, he said, is the media. They're part of a "corrupt political establishment" that conspires against Mr Trump and his hardworking American supporters.

Jerry Lipson, a retired firefighter and Vietnam War veteran from Melbourne, singled out debate moderator Lester Holt as emblematic of the biased media.

"He jumped on Trump, but he never jumped on Clinton for nothing," he said. "I knew it was going to happen. It always does."

His advice for Mr Trump next time?

"He needs to talk more about Hillary's emails, more about Benghazi, where she screwed up," he said, referencing the 2012 attack on the US consulate in Libya in which four Americans were killed. "He needs to come back with more zingers."

Mr Trump likes to boast that he's running more than a political campaign; he's leading a movement. At least in this Florida jet hangar on Tuesday night, full of thousands of screaming, adoring fans in a key swing state, it felt like that might really be true.

Mr Trump concluded his rally with words of warning for the establishment that has mocked him, dismissed his debate performance and downplayed his chances of winning the presidency.

"Washington DC will soon come face-to-face with the righteous verdict of the American voter," he said.

For the crowd in Melbourne, "soon" isn't soon enough.

Follow Anthony Zurcher on Twitter.