I have heard the testimonies of people who have come to the end of their ropes not too much differently than Winthorpe did and it is always in regard to salvation. But there is a type of "coming to the end of our rope" that occurs in the life of every Christian. I remember reading an illustration in a Hannah Whitall Smith book. I will paraphrase it as best I can.
There was a man that was compelled to climb down a rope into a dry well. The rope that was provided was supposed to be of sufficient length for him to reach the bottom. As he climbed down the rope, he soon reached the end of it and, much to his dismay, his feet weren't touching the bottom. His mind raced, "what now?" The well was pitch dark and he couldn't see anything below him. He looked up and could see to the opening of the well and decided to climb up. He climbed up a little way and was soon exhausted and could climb no farther. He lowered himself back down to the end of the rope and waited there. He soon lost all of his strength and let go of the rope just knowing that he was going to fall to his death. He fell about three inches and found himself standing safely on the rock bottom of the well.
God does the same with each of us. He brings us to the end of our rope of self effort, to the end of our struggling, to the end of our pride. God doesn't want us to hang there and struggle on the rope, He simply wants us to let go and stand firmly on the solid rock of Jesus. So you see, the end of your rope is the best place you can be; it's not meant to be a struggle, it's meant to be a blessing and a cause for rejoicing. You are about to enter the rest that God wants for all his Children and all that is required is that you let go and stand on the Rock, to put your faith completely in Him and surrender your work to Him.