You didn't say what engine you have. It is either a problem with your new carb, your fuel, that your air filter base is not mounted to the carburetor or blown head gasket. Compression is relative ya know... :) Possible that your linkage is in correct and the throttle is not being held open?

Running out of gas because of a restricted orifice. Turn mower up on the RH side wheels with carb up (carb always has to be when tipping mower). Remove brass bolt under fuel bowl - do not remove fuel bowl. Clean the orifices in the bolt including one near the end that just looks like a speck of dirt - rod it out with the soft steel wire out of a small wire tie. Blast it with carb cleaner just for good measure. Replace bolt and let the mower down. If the fuel bowl now leaks, tighten the bolt 1/8 turn at a time until it stops. Use Sta-Bil 360 Marine stabilizer in your gas can every time you get gas and you probably won't have any more carb trouble.

@tomplum. The engine is a model LV195EA. Spec: 362001B. DOM: 04078JA1035. Family: 4T9X9 1951BC. Disp: 195 cc.

@1saxman. The carburetor is brand new. The gas is fresh. Tank was drained prior to replacing the carb. Also, if I spray starter fluid in the spark plug, the engine does start for about five seconds. It seems like gas is flowing through the carb for a few seconds but then it shuts off the flow. The engine would not start at all if the carb was plugged, right?

I connected the linkage to the farthest left hole on the carb. Perhaps that is wrong. I'll have to research that.

Just cause a carb is new doesn't mean it's clean

I was hoping to not have to take apart the carb since it is new. I can try that if that is the most likely problem.

OP, before you take the carb off Give the fuel bowl a tap with a screw driver handle. It could just be a hung up float. Check your work. If I am working on something and it doesn't afterward. I know where to start looking. and if you are unsure of a setting . get an explanation or a picture of what it needs to look like. That you can probably find somewhere. on the inter webz

Ken; you seem like a smart guy. Do the quick and easy job I recommended. If it doesn't work, you're only out ten minutes of your time. Plus you learn how to do it as you definitely will need to in the future unless you start using the Sta-Bil now. I knew the carb was new but I theorized that perhaps a little particle of something got into that small bleed I described. When that happens, a wonderful, heavy duty, long-life mower engine simply will not run. It could even be a particle of rubber out of the gas line. It happens.

I cleaned the carb and got it to start. Thanks everyone.