One woman, faced by a crisis, may say confidently: "I will let go and let God." In this case it is a courageous statement of faith that good must prevail, and that any decision she might have made, based solely on her human judgment, could have been unwise. She leaves the problem to God, expecting His guidance on what to do.
In another instance, Let Go and Let God may be a despairing statement of defeatism, an expression of apathy, of unwillingness to play one's role in the task at hand.
Those who simply turn their backs on their problems are not "letting go and letting God" ~ they are abandoning their commitment to act on God's inspiration and guidance. They do not ask for or expect help; they want the whole job done for them.
I cannot simply shrug off the responsibility for facing my problems, however great they may be. True, I need God's guidance, but acting upon it is my job; I cannot evade it without turning my back on life itself.
"Let me not yield to apathy or defeatism, which in and all around me are the evidence of a loving God who will help me in all my need."