Income inequality only really becomes a problem when access to basic goods, services, and blue collar jobs, becomes difficult. Right now it is getting more difficult for lower classes to put food on the table, take care of healthcare, put kids through school (there's increasingly few jobs that don't require college education).
I think if we had a single payer healthcare system, and we reigned in college costs/did a better job of pushing people to trade schools for certain working fields, we'd go a long way towards boosting lower classes. Also, minimum wage should probably keep pace with cost of living adjustments, that just seems like common sense.
None of this really requires a giant income redistribution model. Healthcare changeover would go from private costs, to public costs, and end up covering more people (since middle man profit would be taken out of the equation), trade schools and school loan reform would set less 20 year olds back when they enter the "real working world", minimum wage adjustments would also lift strain, while not costing companies too much (price of goods would go up cents on the dollar from studies I've seen).
The problem is making some of these things happen would take cooperation from many lobbyists in DC, and frankly that's not likely. So we'll just continue going down this road, and blaming every President in office until something gives.