President Obama recognizes that some tax increases are going to be necessary to reduce our national debt long-term. I like his Buffett Rule: that people earning over $1 million/year should pay a tax rate of at least 30 percent. I think this is in line with the literature on optimal taxation (like the excellent Peter Diamond and Emmanuel Saez paper), which not only supports the idea of progressive taxation, but always (to my knowledge) concludes that we should have a tax system that is much more progressive than it currently is.
Mitt Romney's tax proposals would significantly raise the national debt, and are fiscally irresponsible. The assumptions made to argue otherwise are questionable at best. Reagan and Bush after him are responsible for running up the national debt unnecessarily during good economic times. The recession that began at the end of Bush's term has caused the national debt to continue to increase under President Obama, but I think the ultimate cause of that was deregulation, and that increase was necessary during an economic catastrophe. Obama supports regulating Wall Street to prevent something similar from happening again. An increase in tax rates on high incomes will reduce the deficit and will not significantly hurt the economy because people with high incomes are more likely to save their money during a recession anyway. Tax cuts on people with low incomes and direct government spending tends to stimulate the economy during a recession, because that money gets spent, and not saved.
Barack Obama is simply more fiscally responsible and has tax proposals that are more in line with the interests of middle-class Americans, rather than the very rich. His proposals make good economic sense.