Reuters President Barack Obama threw red meat to his political base on Tuesday with a promise to do the nearly impossible: solve the problem of widening US income inequality. Faced with the very real possibility of losing the White House in November, Obama used his State of the Union address to demand a tax increase for millionaires and launch an aggressive campaign arc built upon economic fairness. “No debate is more important,” Obama said early in his hour-long speech before a joint session of Congress. “We can either settle for a country where a shrinking number of people do really well while a growing number of Americans barely get by, or we can restore an economy where everyone gets a fair shot, and everyone does their fair share, and everyone plays by the same set of rules.” In recent months, Obama had made clear he would mine the vein of resentment in America over the growing income gap, the source of inspiration for last year's Occupy Wall Street movement that highlighted the concentration of wealth among 1 percent of the population. But by choosing to make it the cornerstone of his annual speech to the nation, he cemented the theme of working for the 99 percent as his campaign battlecry for the next 10 months. He could not have chosen a better day to contrast his populist ideas with his possible Republican challenger. Mitt Romney, one of the wealthiest presidential candidates in history, released tax returns on Tuesday that showed he and his wife paid an effective tax rate of 13.9 percent in 2010 and expect to pay a 15.4 percent effective tax rate for 2011. Obama proposed a minimum tax rate of 30 percent for people who make $1 million or more a year, a clear shot at his would-be rival, even though he was unnamed in the speech. “I think it's one of the best cards he can play, especially given that Mitt Romney released his tax returns today,” said Henry Brady, dean of the Goldman School of Public Policy at the University of California, Berkeley. __