Is it normal for a graduate student's fate to depend on the success of a breakthrough idea?
Might not be the best response but here I go:

Sometimes, it's better to think of a PhD as a process, rather than as a product. A graduate student's success is never solely dependent on a breakthrough, noble peace-winning result. Rather, it is dependent on a multitude of factors. 

Will you lose your PhD should this result not work out? The short answer: Probably not. 

Will this impact your 'status' at the university? I don't know, I don't think having 'status' is a good thing personally, as I think it creates disjuncture and limits our ability to produce good research when we get so tied up in politics (but I digress). 

The PhD is not going to be your best work should you continue with Academia. Having a masterpiece, or breakthrough result will of course, heightened your prospects (should you be credited appropriately) but this is rare and not expected. The PhD is about fine-tuning your critical thinking and research skills, and prepares you for that road to noble peace winning, but it is not expected that you are producing amazing research at this level. If you do, it's a welcomed bonus. Many academics that I meet look to their PhDs 5-10-20 years down the road and laugh about them. 

To help you not feel so stressed, my advice to you is:

1. Don't measure your self-worth on the success or fail rate of this project

2. Consider your PhD a process and not a product, and remind yourself that the PhD may be your best work (TO DATE) but will not be your best work in 5-10-20 years down the road. 

3. Try to avoid viewing your PhD as something that has to be perfect, amazing and groundbreaking. This isn't to say that your research wouldn't relevant, interesting or groundbreaking in its own right. It just means that it might not be something that extends our knowledge to the point of receiving a Nobel Peace Prize. That also doesn't mean you won't get there either, you've got plenty of time :)   

4. Stay informed about politics regarding status if this is going to impact your employability at your university or other potentials, but try to remain an observer as opposed to some who partakes. Doing so will keep you grounded but aware.