"Right now, it's all allegations, and there is so much misinformation that we need clarity," said Sen. Luz Robles, D-Salt Lake City.
Swallow is under a federal and state investigation over several instances of alleged misconduct, ranging from attempted bribery to influence peddling to acceptance of improper gifts.
He also is the subject of a pair of complaints to the Utah State Bar, and the lieutenant governor's office is in the process of hiring a special counsel to investigate whether he violated campaign laws by failing to disclose business interests and income.
Senate Democrats sent a letter to legislative leaders Monday asking them, when they meet next week, to schedule a July hearing on the Swallow allegations in the Government Operations Committee.
House Democrats have called for the creation of a special investigative committee to get to the bottom of the Swallow matter or, alternatively, to begin the process of impeachment.
House Republicans are scheduled to discuss the potential impeachment in their June 19 caucus.
None of the Democratic senators is calling for Swallow to resign.
"Everyone deserves due process," said Sen. Karen Mayne, D-West Valley City.
Several civic groups and at least one legislator, Rep. Paul Ray, R-Clearfield, have called for Swallow to step down.
Rep. Jeremy Peterson, R-Ogden, has urged the attorney general, who took office in January, to take a leave until the investigations are complete, and Rep. Spencer Cox, R-Fairview, has said lawmakers should seriously consider impeachment as a way to get to the bottom of the allegations.
Swallow's spokesman has said the attorney general did not break any laws and doesn't plan to resign.
Allegations against Swallow
Utah Attorney General John Swallow has come under scrutiny on a number of fronts:
Bribery allegation • Indicted St. George businessman Jeremy Johnson has, at times, accused Swallow of helping to arrange to bribe Senate Majority Leader Harry Reid, D-Nev. Swallow says he only helped Johnson set up a lobbying deal.
Special consideration? • Three Utah businessmen have said Swallow, as a fundraiser for his predecessor, Mark Shurtleff, in 2009, suggested that a contribution to Shurtleff's campaign would win them special consideration if there were complaints about their operations to the attorney general's office.
Rules violation?• At least two complaints have been made to the Utah State Bar, one by the state's former director of consumer protection, alleging Swallow violated attorney-client rules by discussing a consumer-protection case with a potential donor and suggesting the target meet with Shurtleff.
Withholding information? • The lieutenant governor's office is in the process of hiring a special counsel to investigate a complaint that Swallow concealed business interests on his candidate financial disclosure forms, including a company central to the Johnson deal.
Posh vacations • Convicted businessman Marc Sessions Jenson said Swallow and Shurtleff took posh vacations to his Newport Beach, Calif., villa on Jenson's dime while he was free on a plea deal with the attorney general's office. During the trips, Jenson said they pressed him for fundraising help and other financial deals.