How does a project manager handle missing deadlines? Unresponsive team members? Overbearing clients?

missing deadlines are every one nightmare but , if it happened i prefer to make a new schedule in short time to achieve it then check my weak link in procedures or in my team  and fix it .

also most important to make it clear to the Clint if it will effect the project deadline

Missing deadlines are normal in projects. Missing dead line can happen last moment with bad project managers only. Anticipation and planing of the project is key factor to avoid missing deadlines of the project deadlines. However it may happen, in order to dead with already missed dead line as following:

1- Prepare plan B, and Plan C if possible. 

2- Make sure planing is conveyed to all team members and their knowledge about it is in right place.

3- Close monitoring and frequently assess the situation.

4- Be transparent with customer, otherwise it would be more difficult to handle. and show him the recovery plans

 

However again i can tell you good PM always need to anticipate delays as earlier as possible. last moment doesn't reflect the project was under any monitoring.   

To monitoring of daily work progress and compare with daily target than we can identify where did he make mistaks so daily monitoring is the good analysis to improve and achieving our target