National Republicans dispute that Miller has much of a chance, arguing his disapproval numbers are too high to overcome even with support among Tea Party activists.
The GOP likely needs to win Alaska if it hopes to retake control of the Senate.
A poll released Tuesday by the Republican outside group American Crossroads showed Begich in a tight race with both Sullivan and Treadwell. He leads Treadwell by 1 percentage point and Sullivan by 2. But Begich’s lead jumps to 27 percentage points against Miller, who has a 66 percent disapproval rating statewide.
“Miller's not really a concern,” said one national strategist who’s closely following the race. “Begich is going to be a tough campaigner, we know that, and he's found a successful message that resonates well in the state. We're hoping this primary toughens our candidates up and the strongest one hopefully will be in the strongest position to take him on.”
Polling of the race will be difficult to interpret for some time — Sullivan shares his name with the better-known Anchorage Mayor Dan Sullivan (R), who took a pass on running for the Senate.
Sullivan could prove to be a tough candidate. He has deep connections with some Beltway players, and his brother is a top fundraiser for and ally of Sen. Rob Portman (R-Ohio), a vice chairman at the National Republican Senatorial Committee.
At his campaign kickoff in Anchorage, Sullivan touted his “fighting spirit.”
"I have dedicated my life to serving Alaska and America," he said on Tuesday. "I love this state, and I have a passion for helping my fellow Alaskans.”
Treadwell had been highly touted by GOP strategists early in the race, but has struggled with fundraising — he brought in just $170,000 in his first fundraising quarter, and has yet to announce his most recent totals.
The primary has already become a bit chippy: Treadwell has accused Sullivan, who moved to Alaska in the late 1990s, of being a carpet-bagger.
“I would like to welcome my friend to the campaign ... I am confident that my experience and nearly 40 years of work in Alaska, in both the private and public sector, puts me in the best position to make Mark Begich a one-term Senator," Treadwell said.
Democrats described Sullivan as a "D.C. insider and Ohio native" and played up the potential for Miller to thrive as a result of his candidacy.
Justin Barasky, spokesman for the Democratic Senatorial Campaign Committee, said Miller "now has the opening he needs and the Alaska Republican party slides further into disarray."
—This story was originally posted at 9:30 a.m. and has been updated.