Miller, a Tea Party favorite, beat Sen. Lisa MurkowskiLisa Ann MurkowskiThis week: GOP mulls vote on ‘abolish ICE’ legislation Dem infighting erupts over Supreme Court pick McConnell: Senate to confirm Kavanaugh by Oct. 1 MORE (R-Alaska) in a 2010 GOP primary. But he lost to Murkowski in the general election after she mounted a successful write-in campaign. Miller is viewed by many in the GOP establishment as a weak general election candidate against Begich, and could give the state party headaches in the primary.

Begich is a top GOP target this election cycle, but he'll be difficult to beat. 

Polls show he's fairly popular in the state despite its conservative lean, and he announced on Friday he'd raised $935,000 for his reelection, a big haul for the inexpensive state. He now has $1.5 million cash on hand.

Others looking at running against him include Alaska Gov. Sean Parnell (R) and Lt. Gov. Mead Treadwell (R). Treadwell told The Hill in March that he wouldn't run if Parnell did.

Alaska's state GOP has been in disarray as of late. Infighting between different factions of the GOP has led to the ouster of a series of state party heads, with the latest losing her position last weekend. The main schism is between the party's old guard, with Murkowski at the head, and a combination of libertarian-leaning activists and loyalists of former Alaska Gov. Sarah Palin (R), who'd backed Miller in his 2010 race.

This post was updated at 2:55 p.m.