About taking responsibilities

Usually i tend to be a very responsible person but sometimes I just avoid taking any responsibility. Today was one of those days. I was being told that temporary, the project i was working on would fall under my own responsibility. Instead of being proud, the whole thing scared me a bit.
I'd say it is the same in life: sometimes the fact we are assigned a responsibility just pumps up our enthusiasm, as it is a way of recognition of our capabilities to cope with something and at the same time a way of being told 'I trust you can deal with that' - but other times, responsibility is seen as a burden and it just scares a lot. When I am talking about life in general I mean both professional and personal. It is not enough to be a responsible person professional - as well as it is not enough to be responsible in your personal life. We should be responsible of ALL our actions. Is that so hard?