If there's a bump in the night and it's a thug intent on attacking my family, it's my responsibility to deal with it first. That's who I am as the head of the household. I am the first responder, because my other alternative is to be the first victim, either alongside or right in front of my daughter. And again, while you don't expect such an event to happen, and you arrange your life as best you're able to prevent it, there is no such thing as a guarantee.
Now please understand one thing very clearly before we continue.
Mayor Bloomberg and President Obama don't have this issue.
They literally do not care about such things, and they design their life and their public office so as to be able to not care. It is an intentional act they could cast aside should they so choose, but they have not and will not.
Mayor Bloomberg has a small cadre of hired hands who are near and with him literally 24 hours a day. They are armed, all the time, and they are paid to worry about these things so he doesn't have to.
Likewise, President Obama has a literal army of trained, armed soldiers in the form of parts of the military and an entire division of officers (The Secret Service) whose job it is, once again, to make this not his problem for both him and his entire family. Michelle and his children do not have to concern themselves about these issues because there are literally over a thousand others who are paid to take that responsibility -- up to and including eating a bullet in their place.
If you believe that you have a right to life because your creator endowed you with that right, and that this right is unalienable and thus cannot be taken from you (although it can certainly be disrespected!) then it follows that you have not only the right but the responsibility to defend your life. That is, you have the right and the responsibility to deter to the best of your ability any other person who would take your life from you.
You may choose to delegate this responsibility to others, as Mayor Bloomberg and President Obama have, but your right to life is not inferior to theirs. It is equal. President Obama has no more right to live than you do. You are his equal from the standpoint of what your creator, and his creator, endowed both of you with.
So we have established that you have the right to live, as does the President. And if the President has the right to defend his life with deadly force, and indeed the responsibility to do so, then, should it be necessary, so do you.