What is the role of attitude in life?

What is the role of attitude in life? How does how we approach life change our lives?

A couple of days ago I was in a hotel at their free breakfast bar.  I picked up my coffee and spilled it.  The woman standing next to me (I had never met her before) grabbed napkins and started helping me to clean up the mess.  A couple of previously clean paper coffee cups had been splashed, so I tossed them to the trashcan and missed.  She laughed, and said, "Your day is off to a bad start."

My response: "My day has started by meeting a very nice person."  It just popped out of my mouth, unthought.  

Attitude: how we see what is in front of us.  A positive attitude doesn't change that I spilled my coffee.  It did open my eyes to the helpfulness of a stranger.  

Do we only see the negative? Or do we open our eyes among the negative to find the positive? And what difference does that make?