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Mainstream GOP upbeat after sweeping Tea Party

Joe Carr, seeking the Republican nomination for the US Senate in Tennessee, conceded to Lamar Alexander in the GOP primary on Thursday.

Helen Comer/The Tennessean/AP

Joe Carr, seeking the Republican nomination for the US Senate in Tennessee, conceded to Lamar Alexander in the GOP primary on Thursday.

WASHINGTON — Mainstream conservatives ran the table in Senate Republican primaries as Tea Party upstarts lost all six challenges to GOP incumbents, leaving the establishment upbeat about midterm elections and the insurgent movement beaten but unbowed.

Tennessee Senator Lamar Alexander’s narrow win Thursday night and Kansas Senator Pat Roberts’s triumph on Tuesday dashed the Tea Party’s last hopes of knocking out a sitting senator. Earlier this year, incumbents prevailed in Texas, Kentucky, South Carolina, and Mississippi for a party intent on nominating viable candidates and winning Senate control in November’s contests.

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Republicans need to win six seats for the majority. Democrats, with two aligned independents, hold a 55 to 45 advantage.

‘‘The last two cycles we nominated some people who were not the best candidates for the general election,’’ Senate minority leader Mitch McConnell, Republican of Kentucky, said during a campaign stop in Hindman, Ky. ‘‘In 2014, I’m hard-pressed to think of a single state where we don’t have the best nominee possible in order to do what this is all about, which is to actually get elected and make policy.

‘‘We had a good cycle so far; it doesn’t guarantee the outcome,’’ he said.

Republicans blame Tea Party supporters and flawed candidates for squandering the party’s shot at Senate control in 2010 and 2012, especially in Delaware, Nevada, Colorado, Missouri, and Indiana. Months ago, McConnell vowed to ‘‘crush’’ Tea Party candidates, and the National Republican Senatorial Committee invested money, staff, and time, including over 40,000 phone calls in Kansas in the last weeks of the campaign.

Tea Party supporters and other outside groups acknowledged the defeat.

‘‘If you kind of look at this like a baseball game, you guys totally struck out, done, you’re gone,’’ said Daniel Horowitz, a strategist who formerly worked with the Madison Project, a conservative group that have spent money against GOP incumbents.

By comparison, Tea Party supporters and outside groups upended Senator Richard Lugar of Indiana in 2012. The 2010 midterms claimed Senator Bob Bennett of Utah, who lost at a party convention, and Alaska Senator Lisa Murkowski, who later won reelection as a write-in candidate.

But Horowitz and others insist that the numbers fail to account for the movement’s success in forcing incumbents to move right on issues such as immigration, federal spending, and reauthorization of the Export-Import Bank, the government agency that provides loans, loan guarantees, and credit insurance to help foreign buyers purchase American-made products.

Business groups are pushing hard for the bank’s renewal, but conservative groups are opposed, saying it amounts to corporate welfare.

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