Sen. Lamar Alexander (R-Tenn.) yesterday beat Joe Carr in a decisive primary win, continuing a shutout of all tea party Senate challengers. Carr focused on Alexander’s support for the Senate immigration reform bill, and despite the usual cast of anti-immigrant talk show radio supporters, he came up far short. This is yet one more reminder that while anti-immigration reform rhetoric plays well on right-wing blogs, it is not a vote-getter even among Republicans in an off-year primary. Even in red states such as Tennessee, a tea party hard-liner cannot, it seems, gather enough support in a statewide race to best a solid conservative.

Sen. Lamar Alexander (R-Tenn.) campaigns in a restaurant in Lawrenceburg, Tenn., on Tuesday. (Mark Humphrey/Associated Press)

Alexander joined immigration reform advocate Sen. Lindsey Graham (S.C.) in easily dispensing with a more conservative and anti-immigration reform challenger. Both demonstrated that a well-regarded middle-of-the-road senator can win reelection handily if he stays in tune with his constituents and defends his votes, rather than run from them. A long list of “establishment” GOP incumbents – Pat Roberts (Kan.), Mitch McConnell (Ky.), John Cornyn (Tex.), Thad Cochran (Miss.), Graham and Alexander – all survived potential or actual primary challenges.

The final competitive Senate primary is in Alaska, between two mainstream Republicans, Dan Sullivan and Lt. Gov. Mead Treadwell (who is virtually broke and racing to catch the well-funded Sullivan). One recent poll (albeit a robo-call Democratic survey) has Sullivan 6 points ahead. But there, too, the tea party favorite, Joe Miller, who was the party’s nominee in 2010, is trailing badly.

If, as is expected, the tea party is unable to nominate a single Senate candidate (either to unseat an incumbent or as a challenger), its backers will no doubt decry the influence of “big-money” donors. But, in fact, many tea party candidates got ample funding, and they certainly got free media. The problem was both candidate quality and a message and tone that no longer seem to fit the party’s mood. A GOP operative commented, “Good candidates and campaigns win, bad one lose. The DC based for-profit cannibal conservative groups spent over $20 million again Republican candidates and have not a single thing to show for it.” He added, “These groups, like Senate Conservatives Fund, say that winning doesn’t matter, which in some weird way might explain their eagerness to back fringe, irrevocably flawed candidates who now not only are incapable of winning general elections but primaries as well.’

In opposition to former South Carolina senator Jim DeMint’s adage that he’d rather have 30 true conservatives than a majority, Republican voters have decided they can have a majority of rather conservative and electable Republicans.

Republican voters are still angry with President Obama, but they desperately want to win and to end the era of liberal Big Government. To do that, they are banking on center-right candidates with a broad-based message and solid credentials. It is not a coincidence that the party is therefore in a position to pick up a fistful of Senate seats. If candidates such as Thom Tillis (N.C.), Ben Sasse (Neb.), Shelley Moore Capito (W.Va.), Steve Daines (Mont.), Sullivan (or Treadwell), Rep. Tom Cotton (Ark.), Joni Ernst (Iowa) and others can prevail, the GOP will have a majority — consisting of more sophisticated deal-makers and internationalists than have been there in more than a decade.

Republicans may finally be learning critical political lessons. You can’t beat something – even an unpopular incumbent senator weighed down by an unpopular president — with nothing. And, if you win, you better be able to govern.

Jennifer Rubin writes the Right Turn blog for The Post, offering reported opinion from a conservative perspective.