"It is not surprising some members of the public are concerned, given the unfair and negative nature of the news coverage," Swallow said Wednesday. "I have no plans to resign and look forward to being cleared of wrongdoing once the investigation is complete."
Indicted businessman Jeremy Johnson says Swallow was involved in a bid to help pay $600,000 to Senate Majority Leader Harry Reid to torpedo an investigation by the Federal Trade Commission into Johnson's I Works company.
Swallow and Reid have adamantly denied any such scheme. Swallow said he merely helped line up Johnson with lobbyists who could help with the case.
The FTC sued Johnson and I Works in 2010, alleging he defrauded customers out of $275 million.
More than four in 10 (41 percent) of those aware of the allegations believe Swallow acted unethically, according to the poll by Key Research and the Center for the Study of Elections and Democracy at Brigham Young University. And 17 percent believe Swallow broke the law.
Only 14 percent of respondents who had heard about Johnson's allegations say Swallow did nothing wrong.
"More people want [Swallow] to resign than are standing next to him," said Quin Monson, director of the BYU center. "You see Republicans holding back a little bit, withholding judgment, but I think the troubling news will be, as it moves forward, that there aren't a lot of people coming to the conclusion that he did nothing unethical."
The poll asked 500 registered Utah voters if they had heard of the allegations against Swallow. Those who had were asked if they thought he acted illegally, unethically or did nothing wrong. Those who said he acted illegally or unethically were asked if he should step down.
Overall, fewer than 20 percent of the total sample say Swallow should resign. The margin of error for the total survey was 4.4 percent.