"We have got to do this right," Dunnigan said. "It's going to take some money. But believe me, we're going to watch our dollars very thoroughly."
Dunnigan is one of five individuals interviewing 10 major national law firms, finalists vying to serve as special counsel for the investigative committee. A selection is expected to be announced Friday.
Fellows said it's not uncommon for the firms to bill nearly $1,000 per hour. All told, budget analysts are projecting the inquiry into Swallow's conduct could cost up to $3 million.
The investigation is not an official impeachment proceeding, but the fact-finding by the committee could serve as the basis to initiate such a process.
Swallow, speaking Tuesday on KSL's Doug Wright Show, said he is disappointed at the cost and bewildered how he found himself in the current situation.
"All I can hope for is, if they spend this money, they spend it fairly and wisely, they don't have a witch hunt. They don't try to fuel the fire of a media circus that is ongoing right now," said the first-term Republican, who has declined interview requests by The Salt Lake Tribune.
Swallow is accused of an array of misconduct, including helping a major donor to former Attorney General Mark Shurtleff's campaign try to avoid a federal investigation into his businesses, promising special treatment for donors and accepting improper gifts.
In addition to the House investigation, the U.S. Department of Justice, two county attorneys, the Utah State Bar and the lieutenant governor's office all have active inquiries into the allegations.
Dunnigan said nobody on the committee is happy about having to conduct the investigation, but outside of Swallow's resignation, which he said is up to the attorney general, there was little alternative.
"I don't know how we could have avoided it," he said. "I don't think this is something we wanted and looked forward to, but we are going to do our best to be even-handed and fair."
Whatever firm wins the contract will be required to have its expenses approved in advance by Fellows every two weeks. The fees to be charged account for 15 percent of the final scoring for the contract.
Dunnigan said all of the finalists have highly qualified attorneys with experience conducting comparable investigations.
Once the special counsel is hired, legislative attorneys say it could take months to ramp-up the investigation, from getting the counsel hired and up to speed, to getting investigators on the ground and collecting documents and witness statements.
"It's not unreasonable to think we may not be prepared to call witnesses until November or December," Fellows said.
There could be additional delays if the committee's authority to investigate is challenged in court as has been the case in comparable investigations in other states or if witnesses refuse to cooperate.
"Those sorts of things are certainly fruitful grounds for lawsuits, if someone chose to do that," Fellows said. "I don't want the committee to have any illusions at all. It's entirely possible during the course of this process we'll be in court."
Swallow has said he would cooperate with the investigation, although he and his attorneys have expressed concerns about the scope of the inquiry.
The committee is not expected to meet again for another three weeks, Dunnigan said.
"Sometimes we want instantaneous results and we want answers and we want them right now," Dunnigan said. "This is going to be a months-long process, not a weeks-long process."
That means the investigation would overlap with the 2014 legislative session, which Dunnigan acknowledged would put tremendous strain on staff and committee members.
Maryann Martindale, executive director of the progressive-leaning Alliance For A Better Utah, said she would like to see the committee talk less and get to work. After the holidays and legislative session, committee members will be into their re-election campaigns with the matter still unresolved.
"What I'd like to see the committee do, and what I think the public would like to see the committee do, is a thorough, in-depth investigation with some expediency to it," she said. "And I don't think those two things are exclusive, and the committee seems to think they are."