It all depends on the time of day (Morning can mean 2 am or 10 am) and what construction and the rest is going on. There will be traffic probably over the bridge to get to the cape.
Depending on what's going on, there may also be traffic crossing the George Washington Bridge (if you don't have an EZ pass plan on waiting for the cash tools too along the way). If it's a beautiful sunny day like today, there will possibly be slowdowns at all the exits for the Connecticut beaches (exit 18, exit 60 I believe, etc)
It won't be rush hour bad, but you may not go 70 all the way either. The good thing is that's probably not going to be as heavy as a regular Saturday, I think many people will combine either Monday and Tuesday or Wednesday and Thursday with the 4th and make a long weekend so the heaviest day will probably be Sunday.