Begich, the former mayor of Anchorage, stressed how he has worked with his Republican counterparts in the Alaska delegation, which includes Murkowski and Rep. Don Young, and his independent voting record. He's voted against legislation championed by the president, including being one of four Democrats in April who voted against legislation to expand background checks on gun sales.
"Sometimes, being the only Democrat, if it's good for Alaska, it doesn't matter who's sponsoring [the legislation]. I look for issues that matter to Alaska," Begich said.
He added that, unlike Treadwell or Miller, he was born and raised in the 49th state.
"It's been for all my political career something I've strived for: where the common ground is," Begich said. "I think it's being born and raised in Alaska. That's how you grow up. We don't look what party you are from ... we look at what you can do for Alaska."
In 2008, Begich beat Sen. Ted Stevens, R-Alaska, in a tight race with a margin of just more than 3,700 votes. Stevens, who had a 40-year Senate career, was convicted on corruption charges a week before the election. He was killed in a plane crash in 2010.
As with that race, Begich said this one will be a "hard" fight.
Begich might know that it will be difficult no matter what because he's a Democrat running in a red state, but Alaska political observers say Miller would be a much easier opponent than Treadwell.
Ivan Moore, a pollster in the state, noted that post-election polls showed that well more than half of Alaska voters viewed Miller negatively after he lost to Murkowski.
"What that tells you is he is categorically unelectable in a general [election]," Moore said. "Mark Begich is sitting there rubbing his hands at the prospect of running against Joe Miller in the general. He could close his eyes and do it."
In Alaska, Republicans, independents and undeclared voters can vote in the GOP primary.
"There's two uncertainties," Moore said of the GOP primary. "What are Joe Miller's negatives today? Probably not as bad as when he got beat by Lisa [Murkowski] and ... I think the only thing I can assume is Mead Treadwell has done his exploratory committee work with due diligence and found Joe Miller is perfectly beatable in a Republican primary. I think it's going to be tough for [Miller]."
Moore added that the "death knell will come when Republican primary voters become convinced that while they like Joe Miller, he can't win in a general and that will undoubtedly be used by opponents of his."
"Don't vote for him, he's going to lose," is something Moore believes Treadwell and any other opponents will use against Miller.
As for the general election, Moore said, "Mark [Begich] is a good campaigner. He's done this many times before and he'll never be a pushover, but also he's always going to be vulnerable.
"It's a Democrat running in Alaska, so Mead [Treadwell] and Mark [Begich] in a general will be a very well-contested race, and I think when it comes down to it will be close," Moore said.
Another Republican who is considering getting into the race, but has not announced, is Alaska's department of natural resources commissioner Dan Sullivan. Sullivan, Treadwell and Miller have all met with the National Republican Senatorial Committee.