Bramble doesn't like leaving the decision solely up to the executive. "It's the people's ballot, not the party's."
Senate President Wayne Niederhauser, R-Sandy, said that he and House Speaker Greg Hughes discussed the issue during a legislative trip on Thursday and said they would like to put whatever election process that is outlined into statute in a special session, if needed.
"Doesn't it make sense to put it in statute? That's at least what we are thinking," Niederhauser said. "We know we need to sit down with the governor, because it doesn't work unless all three of us are involved."
Alliance for a Better Utah also weighed in on the side of calling a special session of the Legislature to spell out how the election would work.
"The Legislature is the proper body to answer these questions. Otherwise, any election procedures or results could end up in the courts and could leave voters feeling disenfranchised from their rights," said Chase Thomas, the group's policy and advocacy counsel. "For this reason, it's essential that the governor calls a special session to address this issue as soon as possible."
Herbert said he hopes a special session isn't needed, but if it is, he notes he already tentatively plans one in late summer to tweak a new law that makes Utah's drunken driving laws the toughest in the nation.
Utah has replaced a U.S. representative at midterm only once — 88 years ago when then-Rep. Elmer O. Leatherwood, R-Utah, died in office Dec. 24, 1929, at age 57.
His seat remained vacant for more than 10 months. The state at that time went through the normal caucus-convention system, with parties choosing nominees for a special election to complete Leatherwood's term and also the next full term. Voters cast ballots for both on Election Day 1930.
Republican Frederick C. Loofbourow was elected both to serve the last couple of months of Leatherwood's term and his own two-year term, taking office immediately after the Nov. 4, 1930, election. Newspaper archives show he won the GOP nomination by beating two other candidates at the party convention.
A group of Republicans emerged as possible replacements for Chaffetz in the highly Republican 3rd Congressional District, including state Sen. Deidre Henderson, Hughes, state Rep. Dan McCay, R-Riverton, (although he doesn't live in the district), former independent presidential candidate Evan McMullin, Provo Mayor John Curtis and lawyer Damian Kidd, of American Fork. On the Democratic side, Kathryn Allen, a first-time candidate, has raised $500,000 in a viral campaign.
Thursday, Bramble indicated his own possible interest in the race. Asked if he would jump in, Bramble said "not today."
But the past president of the National Conference of State Legislatures offered that he had received 50 to 70 phone calls within 24 hours of Chaffetz's announcement from around the country from contacts in business, politics and lobbying, saying, " 'Bramble, if you run, we're ready to write a check.' But that's not on my radar."
— Senior Managing Editor Matt Canham and editor Dan Harrie contributed to this report.