I had this same problem, and discovered the cause to be the float hinge pin, which would slide out of position and partially free the float from its hinge.
When your car stalls, remove the lower half of the carb and check the position of the float. If it drops down at an angle, your hinge pin may be out of position.
The cure is to flatten one end of the pin in a vise and tap it into position through the carb hinge ear.
Of course, you should first check all the other items mentioned in the previous responses, as well as debris in the secondary well. I agree that vacuum leaks and incorrect float level are most often the cause of idle problems, but you report no problems with your old carb, or with the new one, initially, so you should suspect some issue which developed in the new one after a few miles of running.