How do you handle a heavy workload with many deadlines?

The most important factor in handling a job is proper planning; then comes execution, and then evaluation of the task accomplished. If a person is handling the task alone, he should prioritize and determine what is to be done first and what should follow. Time factor is also significant. To meet the deadlines, one should make use of all effective available tools.

If a team is at work, the leader should assign duties to all and get the work done through proper coordiantion and supervision. 

The main skill on any job is the person should be able to prioritise properly all the work so that none of the important work should missed the deadline, biggest project's deadlines can be met on the cost of low importance deadline.In addition I am aware of the environment where deadlines are not met simply because lack of resources, in that situation the manager or the authorised staff should be courageous enough to take the decision or influence the decision makers in the best interest of the organisation to have more resources (human capital, equipment or whatsoever) to meet the deadlines.

If the management or the authority have broad vision like Mr. Ambani (we know business man from India)  who said "Meeting the deadline is not enough, beating the deadline is my expectation" so the beat the deadline you must be catered with all the necessary resources to make a win win situation for company and employees.