She will aggressively protect them until she is ready to cut the apron strings. So if you are waiting it will be 5 or 6 weeks if you don't intervene somehow.
I have found we can bribe the broody to hang out around us with some scratch or meal worms and it's the best chance for getting the chicks used to humans also (we use finch seed and meal worms, the finch seeds are very small and easy for the chicks to eat). To do so you need to have the broody and chicks somewhere separate of the rest of the flock (for the first few encounters at least). Sit down on the ground with your legs out in front of you or sit cross legged. Sit quietly in the vicinity of the birds for a few minutes and then scatter a small handful of the treat somewhere close to you. Mama hen will see it and check it out and call over the chicks. Just let the mama and chicks eat and scratch undisturbed. If you want you can scatter some more a bit closer and eventually hold your hand down flat on the ground with a few treat seeds in it as the chicks get used to you. Eventually the chicks will get used to you, and begin associating people with good things. After a few encounters like this I have found our broodies and chicks come running to us when we are out in the yard and the more forward little ones will even jump up onto my legs or lap if I am sitting down.
After they are used to humans then you can start trying to get them more tame and used to being handled. I do this by just spending time on the ground with them and having them take treats from your fingers until they are willing to jump onto your hand searching for more. I don't try to pet our birds, but I do like them being comfortable sitting on my lap or being held by myself or my husband. When ever I do hold the birds as youngsters I offer them a couple of meal worms or other treat while they are being held, this helps them associate being held with something good. They don't have to be petted to get used to being handled enough to make it easy to provide basic first aid or other care as they get older.
