I share 279 centimorgans with a 1st cousin in 12 segments. I don't believe that is enough to be considered 1st cousins. She says she couldn't spit a lot.
Would a small amount of spit affect the outcome of the relationship?
The amount of saliva is a factor in whether or not you get DNA results at all. If you have them, that's it. While there is such a thing as "partial results" it's because you need multiple passes of the DNA sequence to make sure there aren't errors. No testing company will give you results if they don't get enough passes. A very small amount of saliva (like if they're taking it from a 50 year old sealed envelope) might have this problem. If you don't have enough saliva for a proper test at a basic genetic genealogy company, they ask you to repeat the test.
In your case, I'm afraid the answer is...you aren't first cousins.
The expected range for first cousins is 553-1225 cM.
One strong possibility is that you are half first cousins, as the range for that is 137-856. There are many other possible relationships with 279 cM, but the others are less likely to be passed off as full first cousin.