90% of carburetor problems are ignition related.
Before you tear into any carb, always check the timing and the ignition system. Ignition probelms can mimic carb problems. Make sure you have the base timeing set properly (with the vacuum disconnectied) and that all the components are operating properly.
I just helped the guy down the street who was having the same problem on his 66 A-code convertible. He came down to ask me to help rebuild his Autolite 4bbl. He had an incredible bog when ever he punched the gas pedal. I asked him if he had checked his timing and ignition. He insisted he had set his timing to spec and that it was all A-OK; definitely a carb problem, according to his buddy at AutoZoo. He was told he might need to rejet the carb. Now why would a car that ran fine from the factory need rejeting? I went to look at the car.
On checking, I found he had not followed the correct timing procedure and had set timing to 8 BTDC with the vacuum connected. To keep the car running he had opened the throttle pretty high, enough to pull the ported vacuum open. The car only had about 12-13" of vacuum at idle and a very sluggish throttle. On a test drive, whenever he hit the gas, the car would sputter, nearly dying. At cruise, it ran on the warm side and got very poor fuel mileage.
When we pulled the dist vacuum line off, we found that his base timing was only roughly
8 degrees After Top Dead Center. It would barely run at all with the line disconnected. What was happening was that with the way he had set his timing, every time he hit the gas, the vacuum dropped and the timing would retard WAY back and the car would barely run. What he thought was a carb problem was really a tuning issue.
First thing we did was replace the plugs. They were black and sooty. They might have been good, but standard plugs are so cheap, why bother. Just replace them. He has a Pertronix, so points are not an issue. Cap a rotor looked good, wires checked out with the VOM.
We disconnected and plugged the distributor vacuum line and bumped the base timing back up to 8 degrees BTDC. The idle immediately jumped to 1200 so we closed the throttle blade to a normal idle position and settled on 600 rpm as a good speed. We plugged the vacuum line back into the distributor and reset the idle mixture and speed.
The manifold vacuum went up to over 18" at idle. Throttle response was crisp, and the car had good power again. The carb kit is still on his shelf, unused and not needed. (BTW, my Crossflow will absolutely SMOKE this "225hp" 289

)
You may indeed have a fuel issue, but always, always, check the ignition first.