Hi Caroline
It could be a number of things, the vet will probably want to do some swabs for herpes virus, calicivirus, chlamydia etc etc.....Thats if the breeder will pay for them, otherwise they'll just be treated with normal anti-biotics until the virus is under control!
URI's (Upper respiratory infections) can be deadly if left untreated as they will progress into a secondary infection i.e pneumonia.
If the kittens have a strong immune system they will respond just fine to the anti-biotics prescribed by the vet, however it will take atleast a week or so to see any improvements. Also all kittens from the litter will need to be treated regardless of whether they show any symptoms of URI, don't accept any rubbish like "your kittens don't have it....they'll be fine!"
The kittens have more than likely picked this up from mum from birth, and just like with humans.....once you suffer from a viral infection it always remains with you and if for any reason your immune system gets run down through stress or poor diet it can flare up again......The treatment for viruses in cats is just the same as for humans in the respect that you can not cure it but instead offer support to immune system via anti-biotics whenever it does return.
For now its best to leave them with the breeder until the treatment is completed and the symptoms subside!
Luke