Ivory urged his colleagues to delay the vote and study how to proceed.
But Lockhart and House Majority Leader Brad Dee, R-Ogden, said House members made it clear they want to begin investigating now.
"We owe it to our constituents to move on. This has been hanging over the heads of every member of government, as well as our constituents, for several months," Dee said. "To delay and do nothing is probably the worst thing we could be doing. What we could be doing now is trying to find out facts."
Rep. Brian King, D-Salt Lake City, argued unsuccessfully for a committee evenly split between Democrats and Republicans, saying Utahns need to know the investigation is above reproach.
"We want to tell the people of the state of Utah this not a partisan or political exercise," he said, adding it's about restoring public trust.
Having more Republicans than Democrats "opens the door to a cynical view" of the committee's findings, King said.
Lockhart said committee meetings would be open, though there might be reason to close some to protect a witness.
At the end of the investigation, the committee will submit a majority and possibly a minority report to the House but not make recommendations. The resolution does not have a specific deadline for the committee to complete its work but includes a Dec. 31, 2014, repeal date.
The U.S. Department of Justice Public Integrity Section is investigating Swallow, as are the Salt Lake County district attorney and the Davis County attorney, both related to his dealings with indicted and imprisoned Utah businessmen.
The lieutenant governor's office is appointing special counsel to look into alleged election law violations. Swallow also is the subject of two complaints filed with the Utah State Bar.
Swallow denies any wrongdoing.
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