Informal conversations with a variety of voters indicate that, so far, many are falling along party lines. Democrats supporting their nominee seem to believe that more is being made of the situation than it warrants, while Republicans are calling for greater scrutiny and raising questions over the apparent secretiveness of the Clinton campaign.
Butch Gudger, a Democrat who plans to vote for Trump, said that his concern over Clinton's health is part of a wider suspicion.
"I don't think we know the whole picture. There's more to the story, and we don't know everything," he told ABC News at a Trump rally in North Carolina on Monday. "I think that she can take a break, she should take a break. But I think there's more to the story."
Dennis McDowell, a fellow Trump supporter at the rally, said that the timeline of events lends itself to his similar suspicions.
"I can't speculate on her health," he said. "I think the press is trying to make it out to be something that it's not."
Clinton supporters seem to feel the incident has been overblown and the Trump campaign is using it to play into a narrative it established.
He added that now "we're seeing evidence of something that possibly might be legitimate. Everyone is preconditioned to think, 'Hey, Donald Trump and the Republicans' narrative about Hillary Clinton's health has been right all along.'"
Clinton and her campaign "didn't do themselves any favors" after her incident on Sunday because they did not immediately release a comprehensive statement about the health scare, Pumpelly said.
"Immediate full disclosure is very important, and they neglected to do that, and now they are dealing with a bigger problem than they would have otherwise," he said, adding that he sees no serious cause for concern about her ability to run a campaign or the country.
Others voters seem to take issue with both candidates' failing to disclose complete medical information.
"There should be disclosures about presidential candidates' health," said David Kunhardt, a Clinton supporter in California. "I think she has done a better job at disclosing than the other guy, and the other guy has proceeded with a comical representation of his health, which adds up to a lie."
Even some Republicans believe that medical disclosures about the candidates should be evenhanded.
"If we're requiring Hillary to get up there with a doctor, then Trump should get up there with a doctor," said Chet Greenwood, a Trump supporter in Vermont.
ABC News' Candace Smith contributed to this report.