For the past 4 days sewage in our appartment (and ONLY our appartment, no one else has been affected), has been stopping up, all during midterm week no less. I’d say about half the appartment’s carpet is soaked up and both bathrooms are covered in dirty water (I don’t even want to know what kind of water it is, but it doesn’t smell good). They came and “fixed” it the day after the problem was reported, but the next morning I took a shower and it flooded twice as bad as it was before. Is it likely they will give my roomate and I a break, or would I likely be successful in asking for a discount?
The answer probably depends on your lease and location. However, I lived in an apartment for about five years, and if this happened to me, I would raise holy hell with the owners (in a civil, fact-based way, or at least try to). If their answers aren’t satisfactory, I’d contact a local renters assistance office (no idea what they’re called, but I’ve seen them mentioned here a lot).
In addition, I think a rent deduction would be fairly probable, since half the rooms are uninhabitable (though I’m sure there’s an exact definition somewhere). Sewer water can’t be healthy either, so maybe if you aren’t aving the problem fixed expediously, a call to your local health department might turn some gears.
All this IMO of course, no idea what the repurcussions might be. 
Maybe you should be asking the landlord, instead of a message board.
And if not a landlord, then perhaps an attorney. If you have sewage backing up and setting into your carpet, then I for one would demand to be relocated to another apartment immediately, or if not that, then a hotel room (while you continue to pay your rent, but the landlord pays the hotel costs) until the problem is resolved.
Of course as I note your location, there may be extenuating circumstances, but I would first try to work it out with the landlord.
Word to the wise: while calling the Health Department is health-wise a good idea if the landlords don’t solve the problem immediately, be sure you have a place to go if the Health Dept declares the place uninhabitable. You will probably have to relocate immediately. As in that day.
It sounds like you are in college. You college most likely has a “community rentals” department or something along those lines. Give them a visit and tell them your situation and they will advise you as to your rights.
It’s certainly also a good idea to document everything: write down the dates and times of any floods, when any repairmen came and what they did, any conversations you’ve had with landlords, etc. Take pictures of the floods, keep reciepts for anything you had to replace, etc.
Even if it never comes down to a hearing, being prepared for one will give you a better bargaining position.
Give the Health and Human Services a call, or whatever you have around.