73 Corvette engine has just quit 2 times on me

My engine seems to get hot and quits on me.  I have spark, and have breather off of it working on it.  I put a new filter inside the carburetor.  It does not want to run.  It turns over but nothing is going on.  I checked the spark from the coil it is firing.  I pulled a wire off of the distributor and he is send fire to the plug.  The only way I can get it to run a few seconds is to pour gas into the carburetor.  It doesn't appear to be getting gas from the fuel pump.  I was going to change out the fuel pump next if you think that could be the problem?  Please let me know your thoughts as I am going to do this in the morning.  Thanks Dean

Check the fuel pump pressure.  Should be in the 7-9 psi range. 

Loosen the fuel tank lid, and see if that helps. It may not be venting thru the emissions equipment properly, creating a vacuum inside the tank. With the top off the air cleaner, once it dies, can you see a spray of fuel into the carb when you press the accelerator? If not, take the gas cap off, and crank on it, to see if you can then get fuel. IF you get fuel with the cap off, you have a venting issue in the emissions department. If you do NOT get fuel with the cap loose, it may well be a bad pump, or the strainer on the end of the fuel pick-up tube(in the tank) is stopped up.

You may want to check the fuel filter at the carburetor 

pull the line off the carburetor, then remove the larger nut to get the filter out

He stated he replaced the filter....but...is it in the correct way? The open end of the filter goes toward the fuel LINE, the closed end toward the carb.  Did you replace the filter to try to fix this issue, or did the issue happen AFTER installing the new filter?