In an interview with South Dakota blog Political Smokeout, which first reported the news of his run, Rhoden was frank in assessing the challenges he'll have taking on the former governor.

"Obviously I’ve got an issue with name ID all across the state," he said. “I intend on spending a great deal of time east of the river visiting with folks and going from town to town, getting my name out and getting my message out."

But he said that Rounds' pledge to raise $9 million by November 2014 "doesn't scare me." Rhoden said, in deciding whether to run, he had considered "what’s at stake in this race and what I could provide that maybe others couldn’t."

Though Rounds was the establishment pick to run for retiring Sen. Tim JohnsonTimothy (Tim) Peter JohnsonCourt ruling could be game changer for Dems in Nevada Bank lobbyists counting down to Shelby’s exit Former GOP senator endorses Clinton after Orlando shooting MORE's (D) seat, he's faced criticism from conservatives, who believe he's too moderate to win the nomination.

A number of other Republicans are also looking at the race, including a handful of former and current state lawmakers.

Republicans are concerned, however, that a contentious primary could cost them what looks to be an easy pickup. South Dakota has turned increasingly red in recent years, and Democrats were unable to get their favored candidates in the race.

Currently only Rick Weiland, a former aide to Sen. Tom Daschle (D), is running for the Democratic nomination.