I agree with what both of you are saying...the compressor will not keep up, there is no question about that and I also agree that the larger the holding tank the longer the compressor would need to run to fill it. A 15 gallon tank at 90 PSI would last about 30 seconds tops with the compressor running. With an additional 45 gallons of holding capacity, with the compressor running would give the user about 2 to 3 minutes of spray gun usage...that should be enough time to put a coat of primer on an engine bay if done in 6 separate pieces (as I mentioned in my original post).
"One suggestion I could make to make life easier on you, (not so much for your compressor) would be to get a larger holding tank...you have 15 gallons now, if you where to add another 45 gallons, you may be able to get through priming 1 of 6 sections without your compressor being able to spit water out through your gun...band aid on a broken leg scenario"
If the OP had a compressor that could handle the job, I'm sure he could put a coat of primer on the engine bay in less than 12 to 15 minutes. I just happy the OP understands that he needs a larger compressor.