Rush Limbaugh and some myopic Democrats would have us believe that most if not all Republicans who have been voting in Democratic primaries are “dittoheads” implementing the radio host’s “Operation Chaos.” Limbaugh has promoted his scheme for months, encouraging GOP listeners to re-register and vote in Democratic contests for the presumably weaker candidate, Hillary Clinton. As the Democratic campaign dragged on, the radio ranter’s initiative became an obsession among Obama backers, who didn’t care to acknowledge Clinton’s lingering appeal among their fellow partisans. John Kerry, who’s still bitter over hits he took from the right during his 2004 presidential run, has championed the chaos concept, especially since Obama came within a whisker of upsetting Clinton in Indiana’s May 6 primary. “If it hadn’t been for Republicans taking Democratic ballots, he likely would have won in Indiana,” Kerry declared, echoing conventional wisdom.

Kerry’s wrong. The “Limbaugh effect” did not tip Indiana to Clinton. Republicans accounted for 10 percent of the state’s Democratic primary voters. Roughly 130,000 of them took Democratic ballots, and exit polls say they split 54 to 46 percent for Clinton. That puts her crossover advantage at around 10,000 votes, less than her winning margin. Even if we assume all Indiana GOP crossovers voted for Clinton with chaotic intent–a dubious assertion, considering her demonstrated cross-party appeal among older women–they did not contribute enough extra votes to account for her narrow victory.

Far more significant than Limbaugh’s gambit is the fact that Obama attracted tens of thousands of sincere Republican cross-overs in Indiana, continuing a trend that has been evident from the start of the Democratic race. Since January–when Republicans who caucused in Iowa as Democrats told pollsters they favored Obama four to one over Clinton–the Illinois senator has been the steadiest beneficiary of GOP crossover votes. That was particularly true in the primaries of states where the presidency is likely to be won or lost this fall. In Missouri, where Obama narrowly beat Clinton on February 5, his strength among Republicans who took Democratic ballots–they favored him 75 to 21–can reasonably be said to have given him the win. In Virginia a week later, Republicans favored Obama 72 to 23. And in Wisconsin his crossover advantage was 72 to 28. Even in Ohio, where Limbaugh pressed his “chaos” campaign aggressively, exit pollsters found that as many Republicans backed Obama as Clinton.

Are these “Obamicans” conservatives who see the Illinois senator as a fellow traveler? There’s little evidence of that. Prominent Republicans who have endorsed Obama sound themes I’ve heard from crossover voters in numerous states. Former Senator Lincoln Chafee says Obama is “the best candidate…to restore our confidence to be moral and just, and to bring people together to solve the complex issues such as the economy, the environment and global stability.” Recalling her grandfather’s concerns about a military-industrial complex, Susan Eisenhower says Obama is best prepared to address the fact that “we are disliked overseas and feel insecure at home…[that] our federal budget hemorrhages red ink and our civil liberties are eroded.”

Obama has consistently been portrayed in most media as more liberal than Clinton, but he has won crossover votes not by triangulating or presenting himself as some kind of DLC “New Democrat.” Rather, he has preached diplomacy, social tolerance and racial reconciliation–themes familiar to old-school moderates and the Rockefeller Republicans so derided by current GOP leaders. That’s something the Obama camp should take to heart as it plots fall campaign strategy. Republican crossover voting has been a constant in the Democratic race. While Limbaugh’s intervention may have boosted Clinton’s GOP numbers at the end, hundreds of thousands of Republicans have been casting enthusiastic ballots for Obama. They have done so in particularly high numbers in some of what will be the fall’s most competitive swing states: Missouri, Wisconsin and Virginia. If they do so again in November, crossover Republicans could be essential members of a winning Democratic coalition.