What class of travel? The amount of time you'd need to set aside is completely dependent on this. If you're coach I would say that 2 hours is an absolute minimum.

On the TSA issue....last time I flew you checked-in and had your bags weighed and tagged to their destination by BA desk staff, as usual. But then you took your already checked bags back and went for TSA screening (the machine and staff were dedicated to BA travellers). Then you stayed with the TSA agent whilst he handed bags off to the BA baggage handlers.

But then the screening procedure has changed at least 3 times in recent years, so it might be completely different today, or tomorrow, or next week.