I understand you're frustrated; I've experienced a similar situation when I first received my MacBook Pro two and a half years ago.
First of all, I am uncertain if you are near an Apple Store. However if you are, they can repair your iMac right in the store. More likely than not you're going to need a new logic board to fix your issue. After the Apple Store officially diagnoses your issue, I would tell them to call you when the part is in (instead of holding onto your iMac until the part arrives). Also speak to the manager to let him know your situation. The manager should be very understanding and try to minimize your time without a computer. Once the part is in, the repair should have a very quick turn around time. It is not unbelievable to think it should be done by the next business day.
If you do not have an Apple Store near you and you're mailing computer in, then I can relate to your frustration. To me anything beyond a day or two without a computer would be unacceptable.
As to it not being fair to have your computer have to be fixed already; that is out of anyone's control. It is not your fault nor is it Apple's fault that your computer already needs repair. It is an electronic and these things do happen, especially within the first couple of months when electronics tend to fail.
Fortunately Apple is one of the best with customer service. If you are getting it fixed at an Apple Store, it will get fixed rather quickly. Much quicker than another competitor from my experience. If you are upset about how long it takes an Apple computer to get repaired at an Apple Store, please never buy a Dell.
Again, while it is frustrating, what do you truly want from Apple. They will fix your issue free of charge as their warranty states. Electronics aren't perfect and it is always disappointing when these things do happen to your new electronics. However, at the end of the day, it is just a computer and it will be fixed soon. There is no need to get so upset about the simple things in life since getting wound up will rectify nothing.