sounds like a clogged main jet. Up in the threads of the jet is a tiny hole that gets varnished shut. A piece of wire from a twist tie can be used to clean it.

Thank you! Do I have to pull the carb from the engine to clean the jet? I don't mind doing it, but I'd prefer not to take extra steps that aren't needed.

No, you don't have to pull the carb to clean the jet, but prop up the fuel bowl so it doesn't fall off. In that little bolt, there is a large hole that is readily seen in the shank, but there is also a teeny little hole that masquerades as a speck of dirt, also in the shank, not the hole up inside the bolt. Poke in there, and try it! This is the standard Tecumseh fix for those engines, for that problem. Also, check the fuel tank cap to see if the cap might be plugged. the cap has to allow air to get into the carb. If the cap is plugged, you will have an engine starving for fuel. It may run for several seconds, then quit, if the cap is plugged. Leetle bugs love to lay their eggs in any little hole. Look at anything that has been laying outside for some time. you might see every hole filled with mud. not the work of children--the wasps and yellow-jackets tend to do that. Dig one open--you might see a full grown wasp in the hole, or nearly so!

Thank you, rustyj14. I already poked small wire in all the holes in the fuel bowl bolt (including the tiny one at the top of the threads and the one running down the middle). I suspected that there might be a fuel cap venting problem, so I ran the mower with the fuel cap loose, but it didn't help the problem. I'll double check the fuel cap anyway to make sure there's nothing blocking the vent.

Tomorrow I'll remove the bolt and poke up into the venturi to see if that helps. If not, I'll pull the whole unit off and spray everything with carburetor cleaner. I've found some helpful videos on YouTube, and among them and with the advice given here I've gotten a pretty good idea about what needs to be done.

Here's a picture of typical jets.

Shown are 3 of the typical jets and the small holes. All 3 are Tecumseh jets. Briggs jets are similar with the center-bottom hole and one on the side. All these holes need to be fully clean and open for the engine to run correctly.
Some jets only have the center-bottom hole.

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Thank you for the pics, baymee!

I pulled the whole carb and cleaned it thoroughly with spray and a small wire. It was pretty clean to begin with, but there was some gold-colored gunk around the bowl gasket that had started dropping into the bottom of the bowl, and I suspected that might be fouling things up somehow. Once I had all the pieces disassembled, the only part that seemed to have a problem was the idle speed screw, which I think had some gunk stuck in the hole in its tip.

Anyway, I put everything back together, and the mower started right up and continued to run well for about 30 minutes of mowing. Hooray.

Thanks again to all who provided suggestions!

Bought a used snowblower with a Tecumsah engine Model HSK 70. Ran 5 minutes and quit. Took the gas cap off and was amazed to see NO VENT HOLE. Solid plastic with a 1" plastic icicle hanging down. Nothing else. Not knowing what else to do I drilled a 1/16" hole in the cap and now it runs fine. What sort of design is this, anyhow? How can you vent with no hole in the cap, and believe me, there is none. Someone educate me, please. tom in Vt.

I believe that the plastic threads in the tank are either thicker or narrower than the threads in the cap, although the same pitch. Therefor the air path is between the threads. I haven't measured them but I don't know of any other way the air can get in.

I had a 1991 Sears push mower with a Tecumseh engine and the gas cap got broken. Found something that would fit it and screwed it on, but the engine would stall after a few minutes. The original cap had some kind of vent mechanism built in, and any old generic cap didn't work. I went and got the right one and voila, it worked.

Another thing is fuel filters. I have a newer Sears push mower (maybe 2015?), had troubles with it stalling after a few minutes. Shop guy showed me that crud gets in the bowl and is sucked up into the fixed metal tube to the carb. No filter anywhere on the machine. When it shuts off, the gas and debris drains back out of the tube and it will start again and run until another piece of crud is sucked up. I cut the rubber fuel line from tank to carb and installed a 99cent disk filter. Works like a charm. Seriously, a $250 mower that doesn't run because they cheaped out on a 99c filter and two hose clamps. SMH