WASHINGTON — Senate Republican leader Mitch McConnell dispatched his Tea Party-backed challenger with ease Tuesday night, and Democrats turned to two women, Alison Lundergan Grimes to oppose him in Kentucky and Michelle Nunn to fight for Georgia, in elections next fall with control of the Senate at stake.
Setting up a third high-profile race, Democratic Senator Mark Pryor of Arkansas and his Republican challenger, Representative Tom Cotton, were unopposed for their parties’ nominations.
On the busiest primary night of the year to date, Democrats eyeing a return to power in the Pennsylvania state Capitol nominated businessman Tom Wolf to oppose Republican Governor Tom Corbett’s bid for a second term.
Republican primary struggles between establishment-backed conservatives and Tea Party-favored rivals were a dominant feature of the evening, as they had been earlier in North Carolina and will be later in Mississippi, Kansas and Alaska. Republicans must gain six seats to win a Senate majority, and party leaders have made it a priority to avoid the presence of candidates on the ballot this fall who are seen as too conservative or unsteady — or both — to prevail in winnable races.
McConnell, a five-term lawmaker and the embodiment of the GOP establishment, won 60 percent of the vote in Kentucky. Challenger Matt Bevin pulled 36 percent.
For Democrats, Tuesday night was a chance to showcase challengers — both of them women — in the rare states where the party has hopes of picking up GOP-held seats.
Grimes, a prize Democratic recruit, piled up 76 percent in a four-way race, winning her Kentucky primary with ease.
She and McConnell wasted no time turning their attention to the fall campaign.
‘‘Make me the majority leader and Kentucky will lead America,’’ McConnell said in an appeal to home state pride, adding that he would use his power to check President Obama’s agenda.
Grimes said Obama was not on the ballot and responded forcefully to some of the campaign barbs that have already come her way. ‘‘'I am not an empty dress. I am not a rubber stamp. And I am not a cheerleader. I am a strong Kentucky woman,’’ she told cheering supporters in Lexington.
In Georgia, Nunn, whose father was a four-term Democratic senator from the state, easily outpaced her Democratic rivals and awaited the outcome of the GOP primary to learn her opponent for the fall.
Republicans set up a July 22 runoff between businessman David Perdue and Representative Jack Kingston — survivors of a seven-way primary — to select an opponent for Nunn.
Along with Perdue, Kingston, and Secretary of State Karen Handel, Representatives Phil Gingrey and Paul Broun also were on the Georgia Republican ballot. The presence of three incumbent lawmakers in the Senate race assured a large turnover in the state’s House delegation come January.
Bevin was backed by Tea Party groups in the state where they made their mark four years ago by sweeping Rand Paul into the Senate.
Outmaneuvered in 2010 when his preferred contender was defeated, McConnell responded this time by running ads featuring testimonials from Paul and by hiring a top aide to Paul to run his own campaign.
For his part, Bevin stumbled through a campaign that included an appearance at a rally of cock-fighting supporters.
Plagued by low approval ratings, McConnell spent more than $9 million through the end of April on his primary campaign, according to Federal Election Commission figures. Bevin spent $3 million, and outside groups poured in $5 million more — a three-way deluge of television advertisements expected to continue through the fall.
The Georgia Senate race was also fiercely expensive — $10 million had been spent on television commercials through the end of last week — and highlighted the divisions within the Republican Party. Perdue relied on his background as a businessman, while Broun and Gingrey ran farther to the right. Handel sought to capitalize on the backing of former Republican vice presidential candidate Sarah Palin, and Kingston had the support of the US Chamber of Commerce.
In Oregon, Monica Wehby, a physician, won the Republican nomination to oppose Democratic Senator Jeff Merkley in a race that GOP strategists hope can become more competitive as the year unfolds.
There were gubernatorial primaries in five states, including Idaho, where two-term Republican incumbent C.L. (Butch) Otter led for renomination.
In Georgia, Republican Governor Nathan Deal defeated two primary challengers. State Senator Jason Carter, grandson of the 39th president, was unopposed for the Democratic nomination.
Republican Corbett’s poor ratings in Pennsylvania drew a crowd in the Democratic gubernatorial primary. Wolf outpaced a Democratic field that included Representative Allyson Schwartz, who began the campaign as the front-runner.
Arkansas primary voters set up a race between Republican Asa Hutchinson, a former congressman who also served in the Bush organization, and former Democratic representative Mike Ross.
Democratic Governor John Kitzhaber of Oregon won nomination to a fourth term. State Representative Dennis Richardson beat five rivals handily for the Republican spot on the ballot.
A smattering of Republican House members faced primary foes, notably Representative Mike Simpson of Idaho, who won handily despite a challenge from a Tea Party-backed candidate.
Challenger Bryan Smith said the incumbent wasn’t conservative enough, and he drew early support from the Club for Growth in a bid to oust Simpson.
Establishment groups rallied behind Simpson, and the Club for Growth quit running television ads for Smith weeks ago.
In Pennsylvania, Chelsea Clinton’s mother-in-law, former representative Marjorie Margolies, lost her bid to return to the House — despite fund-raising and other campaign help from Bill and Hillary Rodham Clinton.
Former Republican representative Bob Barr of Georgia — who once helped impeach President Clinton — fared somewhat better in his comeback attempt for the House.
He ran second and qualified for a runoff.