Australia’s deeply unpopular government further damaged its public image Thursday with a bizarre internal power struggle in which the prime minister was forced to open her job to challengers only to find that no one from her party was willing to run against her. The unprecedented spectacle of a leadership ballot without a challenger adds to the perception of dysfunction and turmoil that taints Prime Minister Julia Gillard’s party and is likely to harm its already dismal chance of holding onto power at national elections in September. Kevin Rudd, the prime minister whom Gillard ousted in an internal party coup in 2010, had been expected to attempt to replace her. For weeks, his backers had been frenetically recruiting Gillard loyalists who are becoming increasing spooked by the center-left Labor Party’s dismal performance in opinion polls this year. But Rudd made a surprising 11th-hour announcement that he would not attempt to return to the premiership by running for the party’s top jo