"McConnell made it very clear early on that he and Republicans were going to take on the tea party, and they have been very aggressive," said Stephen Voss, a political scientist at the University of Kentucky.
A crowded Senate primary field in Georgia makes a July 22 runoff likely between the top two finishers on Tuesday for the right to face off against Democrat Michelle Nunn in November.
The most conservative tea party candidates in Georgia are not among the leaders in recent polls, with businessman David Perdue, Rep. Jack Kingston and former Georgia Secretary of State Karen Handel fighting for the top spots.
In Oregon, where polling has been less frequent, moderate Monica Wehby is considered a slight favorite against a tea party-backed state representative.
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They are vying for the right to face Democratic Sen. Jeff Merkley in the Democratic-leaning state, where problems with the state's health-care exchange have given Republicans hope of victory.
Other top races on Tuesday include a tea party challenge in Idaho to eight-term Republican Rep. Mike Simpson, who has been backed by the pro-business U.S. Chamber of Commerce, and in Pennsylvania to seven-term Rep. Bill Shuster.
Voters in Arkansas and Pennsylvania pick candidates in competitive governor's races.