From a project management perspective, the key is to proactively utilize risk management, issues management, scope management, and proactive communication to your best advantage.
Planning is first on the list in starting a project. This includes risk identification and mitigation. If you do not think you can hit the imposed end-date, now is the time to discuss this to the management and project team. It's better to work together risk resolutions. This process also helps from a communication standpoint to better manage expectations.
Proactive communication can help your team members understand their role and impact of changes. This gives you a strong foundation for the follow-up communications that may be required if the user requirements start to slip.
Manage Issues and Scope
As the project progresses, some project members might end up not meeting their deadlines in spite of risk management plans settled. In this case, you have an issue that needs to be addressed. Issues management (problem identification and resolution) needs to be performed. Get more accountability from your management and the client managers to help resolve project resource problems. They are the ones in a better position to think through these priorities and get the work done.
If the users add more requirements, invoke scope change management and make sure everyone knows the costs to budget and schedule. Don't proceed with the changes unless the sponsor has approved the extra time and budget necessary.
Although it appears that you are being held accountable for events and circumstances that are not within your control, you do have control over the processes you use to manage the project. You also have the ability to manage expectations through proactive communication. You should especially point out cause-and-effect relationships.
When all are said and done, you may in fact not be able to hit your imposed deadlines and budget. However, by utilizing disciplined and proactive project management processes, you will at least have the confidence that you're in the right track. As well, you do a much better job of managing expectations and getting management to be a part of the solution--not just the problem.