Responses to the first two subpoenas are due Friday, and the committee chairman said he expects the panel to receive its material.
To the extent possible, Reich said, his team is coordinating with other investigations of Swallow, so the House inquiry doesn't impede those probes and to reduce the amount of work and cost to Utah taxpayers.
"I want to assure everyone we're very sensitive to those issues," Reich said.
Rep. Jim Dunnigan, R-Taylorsville, head of the House committee, said so far the state has been billed by Reich and his team for $250,000, not including the investigators hired by the panel. The entire probe which could lay the groundwork for impeachment proceedings has been forecast to cost up to $3 million.
Several representatives have called for the House investigation to be put on hold after the U.S. Department of Justice notified Swallow and his GOP predecessor, Mark Shurtleff, last month that the department was closing its investigation and would not file charges.
Dunnigan said lawmakers are fortunate to have experts working with them and that he believes the money is well-spent.
"There are leads worth pursuing, and it's going to take some time to determine what the facts are in the case," Dunnigan said. "I think it is worth continuing. I think the Utah public deserves to know what the facts are and that's what we're going to do."
After a 10-minute public briefing on the status of the investigation, the committee members went into a closed session, during which they expected to discuss legal strategy for up to two hours.
Swallow has been accused of a variety of misdeeds, including accepting improper gifts, helping to arrange deals to shut down a federal investigation into a prominent donor to Shurtleff and attempting to extort favors from an individual prosecuted by the attorney general's office.
Swallow, who has been engulfed in the scandal virtually since taking office in January, has denied wrongdoing.
In addition to the House probe, two county attorneys are working with the FBI to investigate whether any state laws were broken. The lieutenant governor's office has hired a separate special counsel to see whether Swallow violated state election laws. And at least two ethics complaints have been filed against Swallow with the Utah State Bar.
Dunnigan said the committee's investigators are still working on how information will be shared with the other probes.