My advice is that around 1/2 litre an hour is about the right rate (about three of the little white cups you get out of a water cooler - they are 0.2 ltr) - so one of those cups every 20 minutes or so. That way in an 8 hour working day you have downed 4 litres. It is best to take the water on board slowly as the body can only accept and process so much fluid, and if you take on too much you just pee it straight out again. Taking the liquid on slowly means less frequent trips to the loo, less of a bloated feeling, and IMHO it works better.
Drinking enough water to kill is extreme, though it can and does happen. However, if you do take on board too much too quick it can badly dilute your essential body salts which can cause cramps and illness.
I would just keep drinking slowly and not try to "catch up". Get through as much as you can drinking at a sensible rate, and then get back to it tomorrow.
