Before Treadwell can face Begich, he'll have to defeat Miller. The 2010 candidate, who has filed to run again, has some Tea Party support and is poised to be a thorn in the side of the GOP establishment. 

Treadwell is the clear early favorite in the primary — he led Miller by 45 to 26 percent in an early May survey from GOP-affiliated Harper Polling, and 49 percent of Republicans held an unfavorable opinion of Miller in the poll. 

But Miller has more than $400,000 in the bank, enough to do some damage in the primary.

Alaska Department of Natural Resources Commissioner Daniel S. Sullivan (R) is also mulling a bid, which could muddy the GOP field.

Begich said he’d long expected Treadwell to jump into the race, and predicted an ugly primary for the GOP. 

“I think that Republican primary will be crowded; it will also be tough,” Begich told The Hill Tuesday afternoon. 

“You can already see they're starting to do little potshots at each other, so I expect that to continue between now and August. Whoever survives out of that, we'll look forward to that.”

Miller defeated Sen. Lisa MurkowskiLisa Ann MurkowskiSenators press administration on mental health parity Overnight Energy: Watchdogs unveil findings on EPA, Interior controversies | GAO says EPA violated law with soundproof booth | IG says Zinke could have avoided charter flight | GOP chair probes Pruitt's four email addresses GOP fractures over push to protect Russia probe MORE (R) in a bitter primary fight. But Murkowski won the general election as a write-in candidate. 

Murkowski praised Treadwell, who she said she’d encouraged to run for the seat. But Murkowski refused to comment on what impact Miller might have on the race.

“It remains to be seen if we're going to see anybody else, but I'm pleased that Mead has stepped up,” she told The Hill Tuesday afternoon. “I think that, at least what we're seeing right now with Mead's entrance, we've got a good strong candidate, and we'll see if more jump in.”

She also said she wouldn’t get involved in the primary.

“Not in the primary. I've kind of always taken that position — in contested primaries, the best thing to do is steer clear of it,” she said. 

“I learned that from my father, who didn't endorse me in my very first race for the Alaska state legislature because I was in a contested primary. It was good advice.”

Treadwell said his campaign will focus on "Fighting for liberty by reversing the Obama administration’s relentless assault on our families and our freedoms," as well as "fighting for fiscal sanity in Washington, D.C." and "fighting for Alaska."

National Republican Senatorial Committee Communications Director Brad Dayspring welcomed Treadwell to the field.

“Lt. Governor Treadwell is a strong candidate who has already won statewide and is very well liked in Alaska,” he said in a statement. “It's early in the cycle, but no matter the candidate, the path to the majority runs through Alaska and we are going to win there."

National Democrats cast the Republican Senate primary as a "mess" of the GOP's own making. 

"It's not even 2014 and Washington Republicans have already made a complete mess out of the Alaska Senate race," Democratic Senatorial Campaign Committee spokesman Matt Canter said in a statement. 

"It looks like Washington Republicans have bought themselves a primary with two D.C.-friendly candidates running against Tea Party hero Joe Miller. What a mess."