As far as I understand it, you should have nothing left in the tank whenever you do that kind of thing.
I'm new to this training thing and the trainers raised my numbers by 30 watts in one week because they were initially too low and now it's really crazy hard keeping up with it but I can still manage even though I want to quit instantly and my legs feel destroyed while I'm no the bike.

They feel fine the next day so I figure that it's not so bad. So if you're feeling ok the next day and you aren't hurting yourself, then yeah... it's supposed to be really hard. As hard as you can tolerate.