The problem with not enough pressure is that at higher rpm there isn't as much time for the fuel in the pump gallery to fill the individual elements, so you get an incomplete fuel charge delivered to the cylinder.
Detroit Diesel, for example, typically runs from 60 to 80 psi fuel pressure in their two stroke engines. Four stroke requirements aren't usually that high, and will function well with from 15 to 20 psi. You may get away with as low as 10 psi, but it's going to be iffy.
Flow rate is a factor as well, but these engines don't use enough fuel for most pumps to fall behind. The amount of return fuel plays a role as well, some engines need a restrictor on the return side of the fuel system to maintain adequate fuel pressure at the pump.
Chilly