More voters in Wisconsin Gov. Scott Walker's state are likely to be white than in other states. (AP/Rainier Ehrhardt)

In a recent interview with CNBC, Scott Walker offered an unusually frank assessment of his strategy with regard to race in next year's presidential campaign.

CNBC's John Harwood invited Walker to talk about broadening his appeal beyond the white electorate. Harwood noted that the country is becoming more diverse, and he wondered if President Reagan, whose bust Walker keeps in his home, would lose an election today without winning more support from voters of color.

The Wisconsin governor didn't take up Harwood's invitation, according to the transcript of the interview published Tuesday:

The demographics you mentioned, I mean it's an interesting question. The nation as a whole is not going to elect the next president. Twelve states are. Wisconsin's one of them. I'm sitting in another one right now, New Hampshire. There's going to be Colorado, where I was born, Iowa, where I lived, Ohio, Florida, a handful of other states. In total, it's about 11 or 12 states that are going elect the next president.

The implication of Walker's comments -- that although the white share of the U.S. population is decreasing overall, there are still plenty of white voters in swing states -- is correct. As David Wasserman laid out in a recent article for The Cook Political Report, 85 percent of voters in Wisconsin next year will likely be white, far more than the nationwide average of 70 percent. In New Hampshire, Wasserman projects that 91 percent of voters will be white. In Colorado, Iowa and Ohio, his predictions are 76 percent, 93 percent, and 78 percent respectively.

An exception is Florida, where Wasserman anticipates that only 64 percent of the electorate will be white. Generally speaking, though, the crucial states in the campaign aren't as diverse as the rest of the states. These figures might give Walker or other Republican presidential candidates optimism about winning the general election mainly by winning the support of white voters.