I am a trainee developer at a large (~120 people) web agency, about 7 days from passing my probation. I was feeling unwell this morning (Thursday) but I went in anyway because I have a deadline for a substantial project to meet in 4 days time (Monday). I was only briefed on this project yesterday (Wednesday). Work days are only Monday - Friday so technically I only have Friday and Monday to do this. I am still quite ill and the fever and dizziness is only slightly better, so I most probably won't be able to go into work tomorrow.
However, I don't think it is fair to just dump an entire project on me with a deadline I know I won't manage to make. I have voiced this out with the person in charge of this project and he just shrugged it off without offering to help.
I have been criticised by my boss twice during probation because he feels I am not enthusiastic, that my technical skills are much lower than my colleagues (I am a biochemist by training) and that I do not study further outside of work to make up for it (which I do, I left a career in science because I am passionate about programming). So I am afraid that if I continue to be sick (which I can't really help), I might get fired because I was unable to meet this deadline, which is unreasonably set in the first place.
I look after myself well but these past weeks have been suffering from sleeplessness (I won't be able to sleep until 2am and would wake up by myself at 6am, 7am), probably because of the stress.
The only solution I can think of is to go in on the weekends (provided I have recovered), but then would it be rude of me to ask for time off in lieu at the later time?