As a manager, how would you handle a situation where you are running short on a deadline?

Identify what is both urgent and important and prioritise these first.

Thanks to invite.

Re-arrange your sources as per the demand of the task. Don't create the panic, be confident and handle the situation with patience by utilizing the best options to meet the urgency. 

1) Check if task in still achievable in the given deadline.

2) If task is achievable will not seek to delay the deadline and will do the following to get the work done within the deadline.

     a) Gather all the team members irrespective of their core competencies and share about how critical the situation is, and will motivate them to give their best in need of the organization goals and reputation and their self interest.

     b) Will quickly cross skill few members from other core competencies to pitch in and support the existing associates working on deadline.

     c) Request team to work extra hours on week days and also work on weekends and assure them to get compensated with overtime payout and comp off for working on weekend irrespective of the deadline being met or not.

     d) Myself will start working with them on the task to help reduce their work load and accomplish the deadline.

     e) Will meet managers of other teams and request some associates from their team if they can chip in and help our team.

     f) Work from home access to associates who want to extend their support from home.

3) If all these doesn't seem to meet the deadline, will in advance keep informed the stakeholders about the situation and need be will request for additional time to deliver the best quality of work.

in case of enough resources, i will rearrange the resources, overtime for the whole team and complete the tasks on the priority base.

In case of shortages, i will finish the near to completion tasks first.

in both cases i will discuss the situation with the team for the best outcome.

acting by priority, which task is the urgent one

Do the urgent ones.

Achieve what you can achieve.

Have reasonable explanations for the pending jobs.

I will distribute the work in the team of engineers and give them target and bounus

As a Manager I am always organizing activities with related shcedule and enumerates each activity from less priority to more priority, now if you are running short with the committed deadlines despite of how good you are in organizing things, I think you must still do your very best to attain the task no matter what happened with the best of your abilities and resources. If you failed to execute the task with the given deadline, it would give poor impression to your performance as a Manager and people around that depends on you would start to distrust you. So you better be "PRO-ACTIVE" all the time.

use the short time you have with confidence identify all the main points and cover precisely with composure  

•  Need to prioritise the tasks. Most important task and nearer to the deadline has to be done first.
• Review the tasks allocated to the staff member.
• Allocating the task to the staff member having more knowledge and expertise to that task. Providing him full support in terms of guidance/lead and time by withdrawing certain task have a longer deadline and allocating some other team member. 
• Regular monitoring

I would push employees titled for the project in disciplinary actions whenever there is shortage in accomplishments and targets given.

redistribute responsibilities  according to abilities relying on the employee's feedback from previous projects