There are major flaws with this thinking. The biggest is that income disparity is not coming from corporate pay disparities. It is coming from the financial sector which employs few low-wage workers. They are getting rich by gaming the system. Currently the Fed is loaning money virtually interest-free. The hope is that corporations will use this to invest in expansion. Instead it is being poured into the stock market and other investments for expense-free profits. The income gap is not between workers and executives, it is between bankers and everyone else.
Today's Democrats may never have read Marx but they are still influenced by him. The current debate over income inequality assumes tha tcorporate executives are taking a larger share of the profits than they deserve and that increasing the minimum wage will be a zero-sum transfer, taking wages from the undeserving rich and giving them to the deserving poor.
Marx saw workers in competition with factory owners for the profits of their labor. Marxists in general see profits as belonging to the workers and owners as parasites. The whole basis of the communal system (communism) was to eliminate the greedy owners so that everyone could share equally in the profits.
Democrats don't see this because of a blind-spot in their economic thinking. All of them have been influenced by Karl Marx.
To most people with any training in economics, raising the minimum wage that much will have severe effects throughout the economy. Businesses will reevaluate every position and eliminate as many as possible. Jobs that cannot be eliminated will have to be paid for somehow. This means price hikes which will fuel inflation and, ironically, reduce the buying power of those higher wages.
If you ask Americans in general what the biggest problems facing America are, the top two have been jobs and the economy for years. If you ask a Democrat, he will likely say income inequality. They obsess over this.In his 2013 State of the Union address, President Obama called for raising the minimum wage to around $9 an hour. By 2014, he was calling for $10 an hour. This does not reflect inflation. Instead it reflects a movement within his own party.
If Democrats looked at actual statistics instead of Marxist-inspired expectations they might act to cut the money line between the Fed and the bankers' pockets. They might but they probably would not. Wall Street has been a strong backer of the Democrats in general and President Obama in particular which is what caused this crony capitalism in the first place.