Wisconsin Gov. Scott Walker (R), fresh off a solid recall win, brought a simple message to the Capitol today: His successful defense of the governor’s mansion last week gives Republicans momentum to win the Badger State’s open Senate seat come November.

In a half-hour closed-door meeting with Senate Minority Leader Mitch McConnell (R-Ky.), Walker discussed the state of play in Wisconsin as well as the broad political principles that Republicans will need not just to win in his state but across the country. Wisconsin’s seat could be key in McConnell’s difficult calculus to become Majority Leader, with Republicans needing to pick up five seats to edge out Democrats.

“He was actually just more or less asking how things are in Wisconsin now. We didn’t get into the nitty-gritty on that,” Walker told Roll Call when asked whether he got any advice from McConnell. “It’s probably one of the most impressive Republican primaries in the country. We have four strong candidates, and I think the simple reality is that with the momentum we have coming out of [June 5], I think it makes it even more likely that we’ll have a new Republican Senator.”

Walker characterized the evening session in McConnell’s Capitol office suite as “very good” and said the two men spoke optimistically about “how we might in the future have a new member from Wisconsin in his caucus.” He said McConnell told him that Republicans in Washington, D.C., were “thrilled” about his victory.

The Wisconsin governor, who was in Washington today for an event hosted by the U.S. Chamber of Commerce, has emerged as a conservative icon, beginning in February 2011 – when he stood his ground on a bill to curb collective bargaining rights for state employees – up until last week when he fought back a recall attempt that caught the attention of the nation but failed to bring enough Democratic support to oust him.

He said his campaign in the recall could be a template for whichever GOP candidate emerges from Wisconsin’s Aug. 14 primary.

“I think what people are looking for — and I’ve said this about the presidential race, too — if people think I won because the ‘R’ next to my name was ‘Republican,’ then they’re mistaken. What most voters, many who crossed over, the ‘R’ next to my name stood for ‘reformer,’” Walker said. “And for any of those four candidates running for the Senate, as well as Gov. Romney running for president, if voters look at them and say, ‘These are reformers. These are people who are going to change things and improve things, make our children’s and grandchildren’s future better and work for us in Washington,’ then it makes them a viable candidate.”

Seven-term Rep. Tammy Baldwin will be the Democratic candidate for the seat being vacated by Sen. Herb Kohl (D). Tommy Thompson, former governor and secretary of Health and Human Services, is the most prominent contender for the Republican side. But he faces a primary against four formidable opponents.