Thank You for The Question XXXXXXXXXXX,
The short answer is most definely yes, there is a fuel pump to pump the fuel from the tank in the boat to the carburetor or Fuel vapor tank if you have a fuel injected motor....
Give me some more information, serial number mainly, and I will give you a picture...
What I came up with is a 150 Hp EFI (Electronic Fuel Injected) Mercury OutBoard...
The Fuel Pump for the fuel coming from the tank to the vapor separator is in the diagram below....
The fuel primer bulb going "soft" is normal, it is located on the suction side of the fuel pump....If it and the fuel system is running "Dry" this is most likely caused by an air leak in the fuel line system between the fuel pump indicated in the diagram and the pickup tube in the fuel tank....
There are two ways to find the issue, first take the boat to the lake again and when the engine begins to die, start squeezing the primer bulb and see if the engine comes back to life, if it does this will confirm a fuel pump problem, if it doesn't, we will need to replace the fuel line assembly from the engine with a portable 6 gallon tank and another fuel line and try it again...If the engine runs fine with the portable tank and hose, the issue is a air leak in the fuel system in the boat or a bad fuel tank pickup tube or anti-siphon valve...If the engine still won't run right with the portable tank, try squeezing the bulb on this tank, If it now runs correctly the fuel pump is most definitely shot....
When you are doing these tests if you see one drop of fuel leaking from anywhere fix the leak and start over, if there is a small air leak in the system when the engine is running (Indicated by the Fuel leak when priming the bulb) the engine will not keep fuel in the system....
Marine Mechanic
21 Years Experience as Mechanic, 18 Yrs Boat Yard Owner/Mechanic, Factory Certified