Short answer: no. Longer answer: still no. Unless you believe the pseudo-scientific ramblings of psychologist Cliff Arnall, of course, who once developed an equation he thought could predict the day we all feel most depressed.
Based on a whole bunch of arbitrary variables — like "debt", "motivation", "weather" and "need to take action" — Arnall developed the equation for a travel firm, presumably to sell more holidays by capitalizing on our collective malaise. So, yes, you're quite right in what you're thinking: it is bullshit.
Only, in the press, the myth is peddled every single year. Each and every national newspaper will run a story about the fact that the third Monday of January is the day we all feel worst. So much so that it's now commonly referred to as Blue Monday. But given it's based on complete nonsense, why is that?
It's probably something to do with the fact that January is a fairly bleak period: the weather's awful, we're all fat from the holidays, and summer seems a long way off. MAKE IT STOP NOW.
Essentially, the equation provides a great way to revel in our mild unhappiness. Obviously, proper clinical depression is complex, and there is now way in hell that an equation life Arnall's could predict a whole nation's mood.
So, no, today is definitely not the most depressing day of the year. But it is a great excuse to listen to Blue Monday by New Order. That'll cheer you up if you're feeling down, I promise.