With that in mind, in alphabetical order by party, here are the names that have come across our radar during the last 48 hours. Who did we miss? Let us know in the comments section.
Rep. Steve Daines: If you're Daines, the prospect of running for the Senate has to look more enticing than it did as recently as last Friday. With Schwietzer out of the mix, Daines is the highest-profile prospective candidate in either field. He's months removed from what amounts to a statewide win in Montana's only House race, and has $600,000 in the bank. Daines says he is thinking about running, but hasn't decided yet.
"My focus is fixed on serving the people of Montana and doing the job they sent me to do," Daines said over the weekend. "I will continue to give this decision the consideration it deserves, and am still taking time to talk with my family and the people of Montana about how I can best be of service to our state."
The two GOP candidates currently in the race, former state senator Corey Stapleton and state Rep. Champ Edmunds, would be underdogs against Daines. And either or both could conceivably move to the race for Daines's House seat if he gets in.
What's clear is that Daines is the new focal point in Montana politics. If he runs, Democrats and Republicans would have two open federal races to look at. Look for his decision -- whatever it ends up being -- to have a ripple effect in both parties. If he runs, Democrats looking to move up would have to weigh a Senate run against an open House race.
Former governor Marc Racicot: Republicans regard Daines as a more likely candidate than Racicot, but if he says no, look for the two-term former governor to get some attention. He held the state's top job in 1990s, and has been involved in national politics and private sector work in the years since.
State schools superintendent Denise Juneau: Juneau is believed to be one of only two Native Americans to ever win a statewide office in Montana. She will reach her term-limit in 2016, which could invite thoughts about other public offices. Like all of the Democrats currently in the mix, she is a far cry from Schweitzer in terms of name recognition, and would have to build a major profile from scratch in the coming months.
Sen. Max Baucus State Director John Lewis: Lewis has been looking at the House seat currently held by Daines, but given the uncertainty in Montana politics following Schweitzer's decision, he might also look at the Senate. And his connection to the retiring Baucus makes him someone at least worth watching.
(Sidenote: Baucus is also worth watching. Yes, he's already announced his retirement. And no, he hasn't signaled at all that he is backing away from it in any way. But with the thin Democratic bench, there may be some party loyalists who will try to coax him to change his mind. "Unlikely but stranger things have happened," said one Democrat familiar with Baucus's thinking, when asked about the odds of a turnabout. The Democrat spoke on the condition of anonymity to provide a candid assessment.)
State Auditor Monica Lindeen: On the one hand, Lindeen has experience running in federal races, having secured her party's nomination for the House in 2006. On the other, she got beat badly that year by Republican Denny Rehberg. Like Juneau, Lindeen will be term-limited in her current job come 2016, which might prompt her to look for a next step. She told the Billings Gazette Saturday that Schweitzer's decision "gives my husband and daughter and I some things to talk about."
State Supreme Court Justice Brian Morris: A former clerk to the conservative Supreme Court Justice William Rehnquist, Morris was a football standout at Stanford who was nominated to the District Court for the District of Montana by President Obama earlier this year.
Stephanie Schriock: Schriock is the head of EMILY's List and a Montana native who once worked for Sen. Jon Tester (D). She left the door open to a run in May, and her relationship with national donors would make her an imposing force when it comes to fundraising. Of course, Schriock's opponents would no doubt try to use her Washington connections against her in an effort to paint her as an insider.
Lt. Gov. John Walsh: Walsh spent more than three decades in the Montana National Guard and was appointed Adjutant General by Schweitzer. He is still new to the LG's office, having assumed the title earlier this year.
State Sen. Kendall van Dyk: Talk about a guy who knows who to win close races. Van Dyk unseated a Republican by 4 (!) votes in 2010. At 33, Van Dyk is very young, and would likely have to compete with pols far more experienced than him.