Republicans can outfox their own: Call it the Orrin Hatch Rule, named for the Utah senator who won a seventh term in 2012. When conservatives on Hatch’s right came out hard to defeat the veteran GOP lawmaker, he focused early to win their support. The same can be said for Senate Minority Leader Mitch McConnell, who assiduously courted his Kentucky colleague (and Tea Party darling) Rand Paul and hired a campaign manager with Tea Party cred.

McConnell easily beat challenger Matt Bevin to win renomination, but the tougher test will come in the general election against Democrat Alison Lundergan Grimes. Now, McConnell “has to establish a certain amount of political distance from his Tea Party opponent but at the same time try to demonstrate that he embraces some of their key issues,” said Ernest Yanarella, chairman of the political science department at the University of Kentucky.

Business and centrist groups were ready: The U.S. Chamber of Commerce was a big winner Tuesday night, backing McConnell and successful candidates in Georgia, Idaho, Oregon and Pennsylvania. The National Realtors Association and National Retail Federation also helped eight-term GOP Rep. Mike Simpson in Idaho beat back a Tea Party challenger.