How do you manage an impossible target date by the Client?

As mentioned: make clear that it´s impossible. Do it as soon as possible, don´t wait for the delivery date and then surprise your customer.

Assuming you already signed a contract and are in the middle of a project: Give them options. E.g, "we can focus on aspect1, so this will be done in time; or on aspect2. one will be in time, the other one will be done4 weeks after the delivery date".

BY WORKING CALMLY TOWARDS TARGET, WITH PROPER PLANNING AND CONTROL 

First, the question indicates that I have a client and an impossible taget date to manage, which means I'm already awared this job/task, so apologising or rejecting it is not an option.

Considering the fact of late finish beyond the impossible target date, then managing the task and the client properly and wisely could be the only recommended option. This could be achieved through different means and tactics; especially in the early planning stage of the task.

The following tips could give some ideas and examples:

- Make the client aware of the challenge and your initial plans (most propbably tight and conditional) to meet the target date.

- Include the (technical & financial) milestones that require client's input as early as possible and with reasonable but short time intervals in the work plan. Then leave it for Mr. client and propbably he will grant the required time extension or part of it for you.

- Make sure you get client's official approval for the work plan as well as the cash flow projection.

- Including milestones (by other involved parties than you & client) also could help in winning some time.

- Work plan (activities by you) must be realistic with allowance for increaed resources. Also optimize the performance/efficiency of your teams, in order to finish as early as possible regardless of missing the target date.

- Report reguraly to keep the client aware of progress status and make sure you get client's approval for the updated versions of the work plan (time programme) after including any delay that should be recorded once occur.

- Dilevery on stages is always a good suggestion.

- Try to avoid having penalty clauses in contract's with squeezed durations.

If it is clear tha target date is Impossible

First try to educate the client about the impossibilities and the dangers of urgency. then tell him a joke

that A son asked his father for a new Brother, father replied ,Ok i will try but it will take atlest9 months. Son insisted for urgency and told his Father that He is a Contractor so deploy more Labour on it to deliver the Brother quickly . Exactly as it is impossible so many things or tasks cannot be make possible in short span of time despite having resources.

A client that sets an "impossible" date can do so for various reasons. If he is uninformed about how long an activity needs to take place to reach a certain quality of product, then he must be educated. If there is an emegency need for example a  disaster situation aspects of the compeleted service or product that are absolutely essential should be retained and other apsects stripped or deferred.

As with every project the situational context is different, and negotiations will always lead to a middle ground. In most cases clients will listen to professional advice, and if they still do not then there will be trouble at every point. Let them go, they will come back when they realize the soundness of your professional advice.

Impossible! Never sign off the contract. 

Possible with time constraint: Fight with the time. Plan well and ensure you have sufficient resources at hand to meet the plan particulalry time line.

Prepare an effective project plan and discuss it objectively with the client.

Well, if its impossible, then you better convince the client that this is impossible.

If this is not possible, then as Gaurav Khanna, Marc Huddleston, and  Fahad Sattar Mughal said, make it clear that how you are going to achieve that.

i.e. Either putting extra resources on the job, or delivery in phases.

You can hire a contractual employees or increase the number of working hours with a certain limit or distribute task by creating multiple small teams

You may try creating milestones that the client accepts as progress toward signoff, and use a phased approach to project end. In other words, if the project goal is to have a1000 users live, look to redefine live to be more realistic or manageable. First phase live with250, second phase live with500, and so on.

Review and disuss the target with the baseline contract target and date of Client's desired target date and advise the Client possible time and cost impact for his consideration and decision!!