The democratic process is one whereby a localized group gets together to cast votes to determine, by majority, a certain direction or decision. The "democratic process" is not a system of government, which is a misconception held by a vast majority of the population. It is, in fact, only a method of choosing a government, which in our country (United States), is in the form of a republic, not a democracy. This inherently limits the democratic process to localized issues, which includes the selection of candidate to represent us, (hence the term "Republic"). We do not as a country, vote to sign a treaty, such as Kyoto, or to sanction a country like we did with North Korea. If we had a direct voice in the matter, then, and ONLY then would we have a "Democracy" or government system based on the democratic process.
The Questioner asserts that the democratic process is to "keep the Executive Branch... responsible to the Legislative". This is a factual misrepresentation - they are equal branches of government (unless you are referring to a Parliamentarian system, like the one in Great Britain), and to place one "responsible" to the other place one above the other; this is simply not the case in the United States.
The democratic process is nothing like the scientific method (called here, "process"). The scientific method is based only upon known laws, to the exclusion of the unexplainable. Social science, of which political science is a significant discipline, may try to mimic certain procedures of the scientific method, such as the collection and interpretation of data, it is simply impossible to predict human behavior on the democratic level, during the exercise of its singular characteristic - the casting of a "vote" or opinion on a matter.
In order to get more people engaged in the "democratic process", we need to have an informed citizenry that understands the basic nature, characteristics and mechanics of our system of government, which is that of a Republic, not a Democracy. Only then can we truly begin to understand the "Miracle of Philadelphia" that was given to us. Only then will we understand that our voice is limited, by design, to a local voice. Once we understand this we are truly empowered to act as a nation.