I don't think there is much the government can do about income stagnation. As economies become more mature, they slow down, and productivity has limits.
Ultimately, the only way everyone's income can go up is if we can produce more with less input. There are practical limits to this and only radical technology can lead ot large boosts (e.g. robots, nanotech, etc) Until then, the only way for businesses to increase output and lower input is to tap into the huge disparity we have with the third world.
Since most people in the US work in services now, there are further limits imposed. Someone's job at Safeway as a Cashier simply is not going to rise very fast.
Income rose in the top 1%-5% because of a short term demand for college educated labor. During the 80s and 90s, white collar workers saw a huge boost in their incomes. I went from the bottom quintile to the top quintile myself. So did most of the people I know who graduated with tech or mba degrees. But now that market is saturated and quickly being outsourced to India as well.
This is not a "jobless recovery" or "income stagnation". Jobs are being created by US companies and salaries are rising fast for the lowest quintiles significantly, only, it's happening in Bangalore instead of Boston.
In a decade or two, salaries in Bangalore might be high enough, and the dollar might be low enough, that the costs of exporting the labor outweight the benefits, but until then, it is an irreversible process.
Pundits would like to see gains by white collar workers used to boost the salaries of the lowest quintiles, but the result would be disappointing, even if you redistributed every dollar over $50,000 to those below. White collar labor is also stagnated now, and except for investment income, their salaries will not rise at the rate they did in the 90s.
Simply put, there is no justification for significant wagegrowth for a guy working at StarBucks, Walmart, or Safeway. Their economic output does not justify any significant increases. They are at the top of the growth curve already. Likewise, for a software developer who went from $40,000 to $100,000 in the 90s, there is no justification for him increasing to $200,000 in the 00s, since there is an equally qualified IIT graduate in India prepared to do the same level of output at $10,000 or less.
Liberals are too focused on the industrial age, the way productivity was explicitly measurable, and they was a good argument that if you produce X+5 widgets per hour instead of X, you should receive some benefit from the increased. Today, wage growth happened in the upper 5% because a new generation of people started worked in hot new industries. And also because, most of the increase comes from being an investor as well as an employee.
I started out making $20k on my first job, and after 10 years, ended up making 6 figures. I did not do this by "stealing most of the gains" from lower quintile workers. The traditional liberal idea is that company X made a hellavalot of money, but evil CEO Y pocketed most of the money for himself. In the real world, company X was an old-school manufacturing company that got off-shored or stagnated, and investors sold off company X's stock and plowed their money into new startup company Y which employes white collar workers.
Because people in the upper quintiles can shift their capital around, they can plow their money into industries and ride the gain, so their incomes rise even as others stagnate. The lower income people weren't so much "robbed" as simply becoming irrelevent, as capital flowed away from their industry and into new industries.
Because a Japanese Bank (Softbank) funded one of the companies I worked at, does not mean my salary increases were "stolen" from the poor. Instead, Japan's investments in the US simply shifted from blue collar factories into high-tech services.
The 90s was an investment boom, and the growth of the upper class's wages did not come by simply stealing extra output from the wages of the lowest service workers.