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.