As a mid level supervisor, what should be your role in case of a difficult target handed to you and team by higher management ?

I think the best way to do as a supervisor is to know the details of that target. Make list of the one you are hard up and ask help, tips, advices from higher ups or ask suggestions from your team. Explore possible approach on that target, make plans and work on it. 

SWOT Analysis is a useful technique that helps you do this. What makes SWOT especially powerful is that, with a little thought, it can help you uncover opportunities that you would not otherwise have spotted. And by understanding your weaknesses, you can manage and eliminate threats that might otherwise hurt your ability to move forward. If you look at yourself using the SWOT framework, you can start to separate yourself from your peers, and further develop the specialized talents and abilities you need to advance your career and help you achieve your tasks in a quick yet successful time frame.

Simplicity is a great answer to many challenges.

Simplify your target by breaking it down to smaller easier tasks. Once you identify these tasks, you now need to identify the best resources to achieve them, this has to be done based on mutual acceptance of the ones involved, imposing additional work on others would not lead to desirable outcomes, while getting people attached to the task would.

This can be achieved by having people involved in decisions related to these tasks, i.e. timelines, methodologies, etc…   

After getting people on-board, the supervisory support can be critical element of successes. Appreciation, acknowledgment and motivation are the primary functions of a supervisor, especially if the assigned tasks are additional to the regular responsibilities of the resources.

As a Mid level supervisor,I would rather first determine the time line for the completion of the task.

I would then map out strategies and plans on how best to execute the task or meet the set target.

I would share the task among my team members telling them how it should be executed.

I would review the result gotten by my team members.

I would finanlly present the executed task or target to higher Management.

 

When the Higher Management is giving you a difficult target, your role as mid-level supervisor is to disseminate the target and the ways on how to meet the completion and success;  gather and put together each team member's idea and make a decision which is the best way to complete the task with team work and team dedication and unity to make it happen. To such, the difficult situation shall become an easy task when unity to work together is being achieved.

Supervision is a joint that merge top managers and employees, therefore all expected tasks and targets must be difficult confronted by a kind of resistance; to reach a mind supervisor or a team leader position you have to had a super skills that manipulate Orders, Tasks, and Targets from higher level by drawing the right path on the right map to guide your team quickly and easily to reach the goals with a minimum and affordable cost.

Try to balance but situation is extreme see Team is favoured as your success depends upon your team work