The deadlines, Cox said, are meant to "mirror as closely as possible" the standard process.
"This is an election," he said. "It's not an appointment."
Since Chaffetz announced in April that he would not seek re-election and would likely not complete his term in office, Gov. Gary Herbert and state lawmakers have been at odds over the authority to set the procedure for special elections.
In accordance with SB54, Herbert has insisted that candidates have the opportunity to qualify for the ballot by collecting signatures rather than solely participating in the party nominating conventions (where delegates select party nominees).
Herbert has refused to call a special session of the Legislature, despite pleas from lawmakers and threats of a lawsuit. Legislators from both parties want to set specific rules for a special election, including options by some Republicans to turn the decision over to some 1,000 delegates.
Senate President Wayne Niederhauser, R-Sandy, said Friday that although he's mad Herbert launched his own plan, "we're not going to sue him, or try to hinder that because it would only lengthen" the election process.
However he cautioned that the executive branch plan, by diverging from what is in statute, "you expose that whole process to legal and political challenges," he said. "That is our concern."
Niederhauser said the House and Senate have agreed to a plan that would allow party delegates to choose nominees in the next three weeks, and then have a general election on Aug. 15.
"It would actually get someone in there sooner than the governor's plan," he said. "Then we would have somebody [in DC] to vote for things like the budget, maybe some health-reform issues and tax-reform issues. That's our concern: We're going to have a vacancy where there are potentially some major votes."
House Speaker Greg Hughes, R-Draper, earlier this week had signaled a possible lawsuit. He did not immediately return phone calls Friday.
However, Hughes joined Niederhauser, and Democratic minority leaders Brian King and Gene Davis in issuing a statement complaining of executive "overreach."
"Establishing election procedures in law is clearly a role given to the legislature by the U.S. Constitution. Separation of powers is one of the most fundamental principles of our government and a vigilant guard against abuse of power. Nowhere is the executive branch given the authority to establish election procedures."
Utah law states that filling an opening for a U.S. House member requires only that "the governor shall issue a proclamation calling an election to fill the vacancy." Herbert has said that gives him the legal power to set the parameters.
Cox, acknowledging the "rift" with the Legislature, said Friday that "they tried once before already and it failed," referring to a measure lawmakers debated earlier this year to define special election procedures. That bill died.
Chaffetz coordinated with the governor's staff, Cox said, to align his departure date with a feasible special election schedule. That includes up to 24 days for candidates to gather the necessary 7,000 signatures, if they choose that path to the ballot.
Still, Cox said, "that's a tall order in a short amount of time."
It's unclear when the person elected to fill Chaffetz's position would begin serving in Congress. Canvassing after the Nov. 7 election could take up to 14 days. U.S. House leadership would then determine a start date, Cox said. The chosen candidate would fill the seat until the end of Chaffetz's current term through 2018.
"This is the first time in the history of the state that we've had a congressman quit or leave his job," Cox said. "This is not something that happens every day."
Utah has replaced a U.S. representative at midterm only once some 90 years ago when then-Rep. Elmer O. Leatherwood died in office in 1929. His seat was vacant for more than 10 months.
Parties chose nominees for a special election to fill Leatherwood's spot and also the next full term. Voters cast ballots on Election Day in 1930.
Utah Director of Elections Mark Thomas said having voters select a replacement for Chaffetz to also coincide with Election Day this year will save the state money, though he did not have an estimate for how much.
He called the process "the best scenario that we had come up with." Chaffetz's largely Republican district, which stretches from Holladay to Mexican Hat, encompasses seven counties. Thomas said "there's still a lot of work that needs to be done" to get ballots to all of those registered voters.
Twitter: @CourtneyLTanner Utah's condensed election calendar
Friday • Candidate filing began
May 26 • Candidate filing ends
June 12 • Deadline for candidates to submit signatures
June 30 • Rep. Chaffetz steps down, Lt. Gov. issues special election primary ballot
July 25 • Ballots mailed to eligible voters
Aug. 1 • In-person early voting begins
Aug. 15 • Special and municipal primary election
Aug. 31 • Lt. Gov. certifies special general election ballot
Oct. 17 • Ballots mailed to voters
Oct. 24 • In-person early voting begins
Nov. 7 • Special and municipal general election
Source: Utah Elections Office