A model and type # would help. If this is primer type carb (carb on tank model) -it sounds like classic diaphragm symptoms.

Model # is listed as 204210X8C. If by primer type you mean that you have to press a rubber bulb 3 times before starting, then it is one of those. It also does not have an adjustable throttle lever. Thanks

Well, I put the Murray part # into parts look up and it doesn't give the model and type of the engine. That would be helpful. From the pic, it looks like quantum style engine. Certainly the spring and rpm setting is important, but it does sound like the fuel system needs cleaning. Possibly the carb or intake is loose. Are you up for the repair?

I did run a couple of tanks with sea foam in it to attempt to clean things up but it didn't help. With enough direction, I can tinker reasonably well. I just need to know where to start.

Again, I'm guessing what engine you have. If the carb seems loose where it bolts up, could indicate a condition that is creating a vacuum leak. Otherwise, it is clean the tank and carb plus either replace or flush the fuel line- if it has one...

Carb is very tight. One other piece of info to help troubleshoot... The mower runs horribly coming close to stalling the whole time until it gets low on gas when, for the last minute or two, it runs great. Any idea what would cause that?