WASHINGTON — Senate Republican leader Mitch McConnell easily survived a Tea Party challenge Tuesday as voters in Kentucky and five other states went to the polls on the biggest primary day of 2014 so far.McConnell coasted to victory over Louisville businessman Matt Bevin in Kentucky’s Republican U.S. Senate primary.He now faces a more daunting test as the general election campaign begins. Alison Lundergan Grimes, who handily won the nomination in the state’s Democratic primary, is running even with the five-term Senate veteran in the polls as she seeks to unseat a major leader of Congress, something that has been done only three times in the last 20 years.The Kentucky race was one of several Tea Party vs. establishment clashes Tuesday.In Idaho, Rep. Mike Simpson was battling Idaho Falls attorney Bryan Smith for that state’s 2nd Congressional District seat. Smith appeared to be fading; Simpson has reportedly outspent him by nearly 3 to 1.In Georgia, five well-known candidates vied for the Republican nomination to replace Sen. Saxby Chambliss, R-Ga., who’s retiring.Polls suggested that Tea Party favorite Rep. Paul Broun and staunch conservative Rep. Phil Gingrey would fall far short.Businessman David Perdue, stressing his private-sector experience as he bashed all things Washington, had a big lead in polling. His Republican opponents tried vigorously to stagger him, questioning his business record and accusing him of trying to buy the race. But in a year when voters are angry at Washington, his message had been resonating.The Tea Party Express rallied behind former Secretary of State Karen Handel. Also in the mix was Rep. Jack Kingston, R-Ga., a favorite of establishment Republicans. If no one got a majority Tuesday, the top two finishers will compete in a runoff July 22.The winner will face Democrat Michelle Nunn, daughter of popular former Sen. Sam Nunn. She leads most of the potential general-election rivals, though Perdue leads in some surveys.Democrats took the spotlight in Pennsylvania, where voters appeared poised to reject a longtime congresswoman’s bid for the gubernatorial nomination to challenge Republican incumbent Tom Corbett. Rep. Allyson Schwartz fell far behind businessman Tom Wolf, who’d flooded the state with ads stressing his independence from Washington. Also voting Tuesday were Arkansas and Oregon.McConnell’s task now is to woo independent voters he largely shunned as he fought the thunder from the right.Bevin hoped to duplicate Sen. Rand Paul’s 2010 triumph, when Tea Party support helped the Kentucky Republican defeat McConnell protege Trey Grayson in the party’s Senate primary.McConnell, though, has deep Republican roots. He has a strong network of backers, built from his years as the architect of the modern Kentucky Republican Party, the winner of five statewide elections and a veteran of all kinds of state political wars.He knew how to adapt. He made sure that ads and surrogates defined the barely known Bevin in unflattering terms. He hired a top Paul adviser to manage his campaign. He began highlighting his fealty to staunch conservative causes. In March, he appeared before the much-watched Conservative Political Action Conference holding a rifle over his head; it was a gift to Sen. Tom Coburn, R-Okla., a conservative hero for his relentless commitment to their agenda.