Regularly review estimates, deadlines and milestones to check they are still on schedule. If necessary, update the plan with new estimates and tasks and ensure that remaining tasks are necessary and estimates are still valid. Circumstances can change during a project but question every change and always refer back to the original business requirement as a corss-reference.
The timescales must be realistic and, in practise, the project manager will probably have discussed timescales with the team before the schedule was finalised. They will also need to understand the criteria by which each task is determined as complete.