In a situation where the budget is very tight, the best course of action for a project manager is to continuously monitor the project's budget and anticipate potential issues. This proactive approach allows the project manager to identify and address any financial concerns early on, preventing them from escalating into more significant problems. It aligns with the PMBOKGuide's principles of cost management, which emphasize the importance of planning, estimating, budgeting, and controlling costs to ensure that the project can be completed within the approved budget1.
References: PMBOKGuide - Sixth Edition and other standards within the Project Management Institute's foundational standards1.