Does the US government today meet the democratic, social, and deliberative mandates developed at its inception?

Yes, and it meets them more today than it did at the founding of the government.  In 1787, America still had slaves.  Women could not vote.  There was a constant fight between Native Americans and whites over land use and ownership.  While it was not written into the Constitution, many states had property requirements one had to meet to vote or to run for public office.  The government of 2016 is much more democratic than the government of 1787.  Minorities can vote.  Young people who are over the age of eighteen can vote.  There are no property requirements to vote, and in many states you do not even need proof of identity.  Slavery has long since been abolished.  
The original government had little in the way of social responsibility.  The Founders believed that small government was ideal.  However, due to demographic changes and changes to the way Americans work, this changed.  The government has gotten involved in civil rights and workers' rights.  It is also involved in environmental protection and public education.  These additions to the federal government's responsibilities continue to adapt as people feel a need to get government involved.  While some critics of large government are wary of federal oversight, this is one of the consequences of living in a democracy--people vote to uphold their best interests.  

The U.S. Government does meet the democratic, social, and deliberative mandates developed at it's inception.  We cannot deny that even in it's inception, what we know to be government, was even then divided by those who sought justice and fairness for all, and those who wanted to quiet down the outcriers. 
Not much has changed today in that aspect.  What has changed, is the involvement of many other countries, and their influence on our decisions as a lawful country, sometimes taking away from our focus on independent growth as a unified Nation.  
With exponential population growth, we have seen amazing advancements in intelligence by humans, technology growth, and social demands. What started out as a way for the people to be heard in regards to the wants and needs of communities to work harmoniously, has turned into ways for people to get rich, manipulate, and abuse the communities they are "chosen" to protect. Which by any intelligent eye, can be seen as the easiest way to handle an enormous group of people who essentially cannot be "handled."