Many problem exist with the theory, but the largest problem is the slippery slope that allows the lawyers that dominate the political structure in Washington to get their hands into every sector of the economy. Some economists believe that this would eventually degenerate into pure socialism.
In the very recent history of the United States, a recession hit many people very hard. The people hit the most were people in their twenties and thirties. Unemployment within that group is the highest it's ever been, leaving Generation Y extremely frustrated and for good reason.
An unfortunate outcome of this event has led people to look for government for answers. Even though the government itself was the cause of the recession, the lawyers did what lawyers do best and push blame to a group of people that were totally innocent - the entrepreneurs. Successful businessmen were demonized and given the image that they take as much money as they can get and don't pay their fair share into society. This is despite the fact that these very people create jobs, sign paychecks , and provide health insurance for their employees.
Since the people that cause production are under serious siege in America, production is going to slow down, which will cause the recovery to continue to happen at a very poor pace. While government is pushing for consumption, it is demonizing the very industry that allows it to happen in the first place.
Since the Federal Reserve is operating its printing press at full pace, inflation is running rampant in society as the price of everything increases while wages stagnate and savings are destroyed. Consumption is an important part in the economy; but just like it cannot be someone's sole job to eat, the American people cannot simply consume. This will make US currency very unappealing on the global market - just ask Zimbabwe.
In order to consume, America must also produce. Punishing the people that make this happen by over-taxing and over-regulating them will cause them to simply pack up and take their production to other countries, as we see this happening already. The claim that millionaires don't pay their fair share is completely absurd. Their activities benefit society in every way, they should not be punished for being successful.