Small Engines (Lawn Mowers, etc.): Mower starts, then dies, carburetor problems, new spark

Question
Craftsman Mower Model # 917.378350
21" Blade / 6.25 HP Tecumseh

Motor starts when primed properly.
Motor stops 5-15 seconds after starting.

I have done the following:
- cleaned out undercarriage
- Removed and cleaned carb (it was very clean actually)
- Verified float is still good
- Emptied gas tank
- Verified fuel line into carb is clear
- New air filter
- New spark plug
- (lastly) a New Blade

Symptoms persist.  Any ideas what's happening?

Answer

Carb Kevin
You still have carburetor problems try spraying some carb cleaner in to the carb and see it you can get it to stay running that way. When you stop spraying and it stalls you need a new carburetor or a rebuild kit Part # 632809 $11.99   or new carb #640303 $69.99