I tend to agree with Caleb.
I run a ASP.NET server on Linux with mono and Nginx.
It has 48 MB RAM and a 250 MHz ARM processor, and runs PostGre SQL as well.
RAID-2, but no GUI whatsoever of course.
It serves 150 to 200 people at times, and performance is good, site load never take longer than 2 seconds, even under full load. I'd say that's fantasitc for such low specs, especially considering that the database runs on the same system and that PostGreSQL is not the fastest database system I've ever seen.
That's certainly not comparable with the requirements for windows, especially with IIS, which unlike Nginx, has a much high memory requirement, especially when it scales up, but I tend to fully agree with your sysadmin.
Get a profiler, and see where the problem is.