There is no magic number for length of orientation. In my experience, it does help to have a formal set of criteria a new hire has to fulfill before working independently. Does your hospital have such a checklist? Does your policy and procedure manual outline the expected job duties and competencies for a staff RN on your floor?
If your hospital does not have a formal list, sit down and make your own. What are the everyday nursing duties that need to be done? What sort of major skills a nurse needs to have in order to hold his/her own on your floor ex. IV insertion, basic EKG knowledge, ACLS etc.?
See how your performance matches up to these lists. You may find that you have hit on all the major points. There can be a huge, huge gulf between competency and confidence level. Your managers may have deemed you competent enough to go on your own even if you are still nervous about doing things.
If you do see areas where you have zero experience on and urgently need training on, bring that up with your managers or educators. I think it is far more helpful to be specific on what you need as it relates to being an active member of a team instead of simply asking for more time.
I hope that helps and please do update us