Mike Cordeiro, a libertarian-leaning owner of a small Florida cannabis company, woke up on Wednesday morning feeling great. He has long thought the American status quo needed a good shaking. And with the victory of Donald J. Trump, he was optimistic that big change was in the offing.

“It’s amazing,” Mr. Cordeiro, 42, said of Mr. Trump’s victory. “I think it’s a beautiful thing, the people he has with him: Elon, Tulsi, Vivek, or whatever his name is. I think it’s going to be a game changer.”

As tens of millions of Americans trudged off to start their Wednesday with hearts full of fear, anger and dread, a little more than half of the nation’s voters — over 71 million — were feeling something between cautious optimism and flat-out ebullience over Mr. Trump’s decisive victory and return to the White House.

For the moment, among the Republican candidate’s supporters, the feelings of relief and joy were clear. Less clear were ideas about where the mercurial Mr. Trump might take the country, policy-wise, though bedrock Trump campaign promises to fix the economy and immigration had obviously resonated.

On Tuesday evening in North Carolina, Debbie Earp, a retired executive assistant, left a watch party in Raleigh for Mark Robinson, the embattled Republican candidate for governor. She was sad to see him lose.

But she and a friend went home and stayed up to watch the presidential results trickle in, their excitement growing as it became clear that Mr. Trump had taken the lead.