However, given the realities of how Congress works, I personally have no trouble using the instruments available to stop the even more undemocratic influence of money in politics, which IMO is what this whole process is all about.
A filibuster calls scrutiny on the law in progress and being able to run a filibuster signifies strong support.
http://thehill.com/homenews/senate/186133-reid-triggers-nucl...
The major benefit of it is that it prevents (in it's present day form) small majorities from passing important legislation. You need at least 60% in the Senate.
I sense that this was said without the slightest hint of irony.
Keep in mind the Senate was not elected by direct vote until the 17th Amendment was ratified in 1913. Instead it was up to each State to select their two Senators and was never meant to be a democratic body.
The founding fathers were very, very, very well educated so they pretty much found all the ways liberty had been subverted throughout history from Greece through the Roman Republic (the Romans themselves were extreemly paranoid about one person holding power) and its fall into the Roman Empire, all the ways the kings of England had subverted the people liberty (fun fact, you can plead the fifth, have a the right to speedy and public trial, etc as a way to prevent another Star Chamber).
In summary, yes it is undemocratic. But democracy is potentially at odds with liberty and freedom. And the Founding Fathers backed liberty over democracy.
People like it because it makes the distinction between having a majority (51% of the Senate) and a mandate (60% of the Senate).