Seelig said the Democrats aren't calling for Swallow to take a leave of absence, because legislative counsel has told them there isn't a formal process for him to do so.
"In addition, there is something very wrong telling the public, particularly the working public, that we're investigating somebody because of questionable behavior and then telling them we're going to pay him for [being on leave]," she said. "His decision to resign or not is up to him. Regardless, we would still like an investigation because this is not just about the attorney general."
This move marks the first time that House Democrats have taken a unified position on the Swallow scandal since the allegations began to roll out six months ago.
Seelig submitted a guest column to The Salt Lake Tribune this week.
"We resolved that because the attorney general asserts that he is innocent of any wrongdoing and has declined to resign," she writes, "we now believe the only reasonable course of action is to initiate a formal investigation."
Meantime, the liberal-leaning group, Alliance for a Better UTAH, said Thursday that Swallow's misconduct warrants impeachment but urged him to resign and spare Utahns the cost and hardship of a such an undertaking.
"Swallow has insisted that he has not broken any laws," the group said, "but by repeatedly making this statement he is showing his gross inability to grasp the core of the issue his deliberate and willful ignorance of ethical and principled behavior befitting an elected official."
Earlier in the week, the Sutherland Institute, a conservative think tank, also called for Swallow to step down.
Swallow is the subject of an investigation by federal and state authorities into a series of allegations, including that he helped broker deals to assist a businessman suspected of defrauding thousands of customers and that he promised protection to potential campaign donors to his predecessor, Mark Shurtleff.
House Speaker Becky Lockhart, R-Provo, said the Democrats, while a minority, represent an important voice in the chamber.
"I wouldn't discount [their position]," she said. "This entire process is about restoring the public trust. This is about the House of Representatives potentially doing something, not one party or the other party."
In recent weeks, Lockhart has sent House members from both parties three emails with information on the impeachment process.
Rep. Paul Ray, R-Clearfield, has called on Swallow to resign or take a leave. Rep. Jeremy Peterson, R-Ogden, has also said Swallow should take a leave. Rep. Spencer Cox, R-Fairview, has said many lawmakers would like to see Swallow resign and that the House should seriously consider impeaching the attorney general.
Swallow's spokesman has said his boss hasn't broken any laws and has no plans to quit.
Seelig said the Swallow saga points to the need for ethical reforms that Democrats have pushed for the past several years.
She criticized Republican legislators for meeting privately with Swallow to let him respond to the allegations, including a private session Wednesday with several lawmakers that was canceled. Reporters were to be allowed at the event, but were told it was to be off the record.
"These secret meetings that are going on are offensive," she said. "I don't know whether or not he's trying to strong-arm his colleagues or just lobby, but I don't understand why we can't have that conversation in a public fashion."