PHILADELPHIA (TheStreet) -- There is real anxiety among Democrats over whether Donald Trump might edge out Hillary Clinton for the presidency, especially as the Republican nominee's economic message encroaches on themes of their own.

Democrats are celebrating the former secretary of state's coronation as their party's presidential nominee here in Philadelphia at the Democratic National Convention this week, but they know they've got a fight on their hands in the months to come. Trump has seen a boost in his poll numbers after the Republican convention in Cleveland, and many are beginning to see him as an increasingly realistic threat.

"I'm scared to death, of course," said Lana Slavitt, a delegate from Minneapolis. "If people stay home and don't care and don't get involved, he could become president."

"I'm worried about Donald Trump," said Laura Calvo, a superdelegate from Oregon. "That side of the aisle, their biggest tool is to create fear in people, and fear is a great motivator for a lot of folks, and so he speaks to that."

"It's a real challenge for us, I'm not going to lie to you," said Cherri Senders, publisher of Labor 411 and communications consultant for labor unions and nonprofits.

Trump's populist message makes parts of the Dems' usual economic argument difficult to make. He has embraced an anti-trade argument at the center of his campaign and pledged to leave entitlements untouched.

"Trump has made very clear that he will try to woo swing blue-collar voters by sounding economic populist on things like opposing the Trans-Pacific Partnership and saying no to social security cuts," Adam Green, co-founder of the Progressive Change Campaign Committee, the progressive political action committee that coined the term "The Elizabeth Warren wing of the Democratic Party."

Moreover, Clinton has struggled to woo some Bernie Sanders' supporters who don't see her as leaning far enough left. Green said he believed progressives had been successful in convincing her to adopt a more Sanders-esque message and is hopeful she will continue it into the general election.

"So far, she's keeping the volume high on big, bold progressive ideas," he said.

Brad Schwanda, a delegate from Oak Creek, Wis., and member of the United Auto Workers union, acknowledged there's a fear in every election that one's preferred candidate won't win. He admitted Clinton hadn't been his first choice for the presidency, but the GOP doesn't appeal to him, either.

"For a union member, for myself, I know that part of their platform is a national right to work, and I'm totally opposed to that, so that's a deal breaker for me," he said. Right to work laws guarantee no one can be compelled to join a union or pay dues.

Democrats believe they have a strong economic case to make to continue in the White House -- they just need to make sure they make it.

"The jobs situation speaks for itself," Slavitt said. "We've seen more job growth in the last five years than we had seen in 15 years prior, and that's a testament to President Obama. She's going to bring more of the same."

"We're coming back, and progress is being made," Calvo said.

Still, they are aware it is an uphill battle. Not only do Democrats have to make their argument, but voters have to research and listen.

"If you're a voter, you really need to look into what you're voting for -- it's like food, you've got to read the label to see what's really in there. I think Donald Trump does a lot of false advertising," Calvo said.