It is always a good idea to change the needle and seat when rebuilding a carburetor. When overhauling a Tecumseh carb, I always do it. The previous poster gave a good description. Just to clarify though, a failed needle and seat will not cure a "running lean" symptom. ( that I am aware of) If the needle and seat has failed it may show signs of running "rich", not "lean". You may also see fuel coming out of the air cleaner, or worse, fuel may be leaking out of the carburetor and ending up in the crankcase. There is a chance that if the needle and seat has failed, the carburetor will flood and the excess fuel can go through the intake manifold, into the combustion chamber, and end up in the crankcase. If this happens the gas will act like a solvent and cause the viscosity of the oil to change. Could end up thinning the oil to the point where the engine overheats. Pull the dipstick, does the oil smell like gasoline? Does the oil appear to be over full? Is the gas tank dry, even though you filled it? The easiest way to check if the needle and seat is functioning is to use a pressure testing gauge. If you don't have one, the next best thing would be to hook the gas tank up to the inlet, look through the throat of the carburetor and see if gas is coming out of the emulsion tube. (usually a brass or plastic tip sticking up in the throat.)
Anyway, back to my original point, replacing a failed needle and seat will not cure a "running lean condition", but properly setting the float height can. So can properly cleaning the carburetor. As the previous poster suggested, ultrasonically is the way to go. Even after that I still pass carb. cleaner through each passage so I can visualize that it is open.
Lastly, I don't believe that you stated weather or not this surging happens at high speed, low speed, or both. If it happens at high speed, no-load, I will also suggest that the you check the rpm's of the engine. If the rpm setting is in excess of the recommended setting it could cause surging. I.e. if Tecumseh says the setting should be 3,600 rpm and it is set closer to 4,000, then that over-speeding can cause the surging and other, more serious problems.