If candidates receive 60 percent of delegate votes, they advance to the Nov. 4 final election. Otherwise, the top two face off in a June 24 primary.
Saturday may be the last time the conventions wield such power. A new law will allow candidates in two years to avoid the convention system and appear on the primary ballot by gathering signatures from registered voters.
However, Utah Republican Chairman James Evans has said his party may challenge that law in court, contending it interferes with how that party chooses its nominees. Supporters of the new system contend convention delegates are more ideologically extreme than most Utahns, and select nominees outside the mainstream.
GOP delegates Saturday will consider a resolution arguing that the change in the convention system is unconstitutional. They will also consider a measure calling on the Legislature to make races for all school boards partisan and another supporting transfer of federal lands to states and declaring that Utah should act to protect its sovereign rights.
4th District • The state's most expensive race so far is to replace retiring Rep. Jim Matheson, D-Utah, and Republicans and Democrats have convention contests for the seat.
Republican Mia Love, who narrowly lost to Matheson two years ago, seeks to become the first GOP black woman in Congress. She has raised more than $2 million this election cycle and still has $632,000 in the bank.
Facing her is Bob Fuehr, a former executive with US West, who is financing his candidacy out of his own pocket. He has loaned $281,000 to his campaign, although he has repaid himself more than $90,000 of that.
"I'm excited for convention. I really can't wait. It's been a lot of fun for me, and meeting delegates is my favorite part of the campaign," Love said. She adds she has met so often with many delegates "that I've gotten to know them very well. They've become personal good friends of mine."
She said the biggest issues for her and delegates include "the national debt, deficit spending and, of course, Obamacare. They, like me, are worried about the overreach of the federal government." Love adds that she is "taking nothing for granted" but feels from meetings that she has strong support from delegates.
Fuehr said his business background is a key advantage.
"This is the time to send someone with real experience and real accomplishments to Washington, D.C., to better this country. Sound bites and inexperience have been contributing factors to the mess we are currently in."
He said he has been holding nearly daily meetings with delegates discussing the economy, jobs, immigration, public lands, health care and political integrity.
On the Democratic side, Doug Owens the attorney son of the late Rep. Wayne Owens, D-Utah is a heavy favorite against retired engineer Bill Peterson. Owens has raised nearly $133,000 from Democratic power brokers. Peterson has not filed a disclosure form.
Owens said he has spent little on the convention race because Peterson "has not been campaigning at all, so we have been saving our resources" for the November election.
"People are crying for someone willing to work across party lines to do the business of the country and not just hold their breath until they get their way," Owens said. "I'm not the kind of person who supports a government shutdown to make esoteric points."
He also said he chose to run because the American dream is disappearing, and he vows to work to improve the economy and help the middle class.
Peterson is campaigning on one major issue: reducing the deficit. "The deficit is the imbalance of trade. It's $6 billion a day," he said. "I've been working on this for 20 years." He adds that Congress "has about 180 lawyers, and no engineers. I'm an engineer … so I can look at things scientifically." (Congressional Quarterly Roll Call reports Congress has six engineers.)
Other congressional races • Republicans and Democrats also have convention contests in the 1st Congressional District, where incumbent Rep. Rob Bishop is seeking a seventh term against David Yu-Lin Chiu.
On the Democratic side, former Democratic nominee Donna McAleer a West Point graduate, business executive and former world-class bobsledder has been in a hotly contested race with Ogden physician Peter Clemens. McAleer has raised nearly $80,000 this cycle and spent $37,600. Clemens raised about $70,000 and spent about $14,600.
In the other two U.S. House districts, only Republicans face convention contests.
Rep. Jason Chaffetz, R-Utah, is seeking a fourth term in the 3rd Congressional District against photographer/entrepreneur Mark Hedengren and software entrepreneur Robert Stevens.
In the 2nd Congressional District, Rep. Chris Stewart, R-Utah, is seeking a second term against former prosecutor Larry Meyers, former radio producer Vaughn Hatton and Zachary Hartman,managing director of a real-estate company.
Democratic chairman • Former Salt Lake County Mayor Peter Corroon and Brigham Young University political scientist Richard Davis are vying to become chairman of the Utah Democratic Party, replacing Jim Dabakis, who stepped down for health concerns.
Corroon has stressed his experience, while Davis said he may help attract more Mormons to the party.
"I have run a government and have run several campaigns," Corroon said recently, adding that his experience on his losing gubernatorial campaign helped him know Democrats around the state, and he seeks "a 29-county plan to ensure the statewide party is giving counties the tools they need."
Davis said that, as a BYU professor, he is well positioned to continue sounding a message from Dabakis "that you can be LDS and a Democrat. Well, I embody that. I think I can say to Utah voters who are LDS, 'Look, it is possible to do. You don't have to be non-LDS or liberal. Democrats have a big tent.' "
Legislature • A dozen multicounty legislative races 11 Republican and one Democratic will also be up for convention votes. Legislative races for seats entirely within one county were previously narrowed by county conventions.
One of the more interesting contests is in House District 69, where incumbent Rep. Jerry Anderson, R-Price, faces a challenge by former Rep. Christine Watkins (who switched to the GOP after serving as a Democrat) and Roosevelt car dealer Bill Labrum who has outraised both the current and former lawmaker.
The winner among them will face yet another former state representative, Democrat Brad King.
Two GOP convention races could determine final winners, because no candidates from other parties are running.
That includes a contest between incumbent Sen. Evan Vickers, R-Cedar City, and former Sen. Casey Anderson. The other is for the House seat of retiring Rep. John Mathis, R-Vernal, between rancher Scott Chew and optician Tod Tesar.
Several other incumbents faces challenges Saturday, including state Sens. Kevin Van Tassell, R-Vernal, and Daniel Thatcher, R-West Valley City; and Reps. Mel Brown, R-Coalville, John Westwood, R-Cedar City, and Kraig Powell, R-Heber City.
• Utah Republican Convention, 10 a.m., South Towne Exposition Center, 9575 S. State St., in Sandy.
• Utah Democratic Convention, 10:30 a.m., Calvin L. Rampton Salt Palace Convention Center, 100 S. West Temple, in Salt Lake City.