Check your fuel pressure.

Sounds like your idle adjust is set too low on the carb.

From: u23084@uwe (Carolina Girl)

I have a 1966 Mustang with a V8 289 engine. It was recently tuned up and
was running well until this weekend. Now, it cranks easily, idles a
little rough, and operates fine at a high speed. But when I let off the
accelerator, the engine cuts off. If I deaccelerate and put it in
neutral and rev the engine, I can keep it going. But as soon as I give
it gas, it shuts off again. Any idea what is going on? Thanks.  

=======
on the old carb units,  there are six individual systems that make up
the carb.   they all work together, and when one of the systems act up,
we tend to say the word, 'carb'  instead of the single system that is
giving the trouble.

as you have pointed out,  everything is working except the idle system.
that is where you need to look for the problem.

you say if runs fine when you are using the partial and main metering
systems, the accelerator pump system, and full throttle system.

what happens is when you let off the gas, is that it shifts the
responsibility of the carb back on the idle system, which it is failing,
thus causing the engine to die.

some of the problems in the idle system, can be everything from mixture
screws out of adjustment, fuel bowl level is not correct, (included in
this is dirt sticking the needle valve open), or to much air mixing with
the fuel (leaking gaskets)   there are more things that can cause this,
but this is a start.  hope it helps.

~ curtis

knowledge is power - growing old is mandatory - growing wise is optional    
"Many more men die with prostate cancer than of it. Growing old is
invariably fatal. Prostate cancer is only sometimes so."
http://community.webtv.net/PALMER_ENT/doc

accelerator pump...small diaphragm on the front of the carb..spits a
measured amount of raw fuel into the systems to overcome the tempaory lean
condition when you step on the gas pedal.