Here's the deal with my Sears mower. I've checked the feul, spark plug, air filter and now I believe it's the carburetor. When I pull the chord, the mower turns over and sounds like it's starting, but almost immediately shuts off. So, now when I pull the chord, I immediately reach down and press the primer pump and the mower will keep running until I stop pressing the pump... is this a gas line or is it the carburetor? Suggestions?

Could be the fuel line has a crack in it and allowing air to suck into carb. But it sounds more like the carburetor

Try some carb cleaner in the bowl and see if it smooths it out.

If you could post all the No# on the engine may be able to get a parts manual so you know what's what on the carb..