|It sounds like you are feeling as if your list of problems to solve has grown beyond the possible, yes?|
I took over a job from a colleague at an office in San Francisco. On day one the employees lined up outside my office door. I asked somebody that I knew from the office, "what are they doing?"
She said, “They're here because they want you to solve their problems.”
One-by-one they came in and said, "I have this problem", and then they turned to leave.
That's called dropping the problem like a hand grenade on the managers desk and expecting that to be solved before it blows up. So I handed it back and said, "you haven't done your homework. Go back and think about what the options are. Think about the pros and cons of those options, then come back, and we'll talk."
Notice that it's now collaborative decision-making about solutions and options, not a subtle (or volatile) hand-off.