It is the tech lead's job to manage the expectations of the PM. It is the PM's Job to push the project along and get it done right, as fast and as they are able. If the PM has waited until a week before the deadline to try to add people to the team then the PM has already failed their job.
As a tech lead these are some tips for improving that:
- Require any requests for completing "More Points" to be specific requests for which stories they want to see prioritized over the current work.
- Explain that you do the work as it is prioritized on the board. That your team works as fast and diligently as can reasonably be expected, and that if the PM has concerns about specific team members not pulling their weight they should address those with the Team Lead.
- Suggest that if your PM wants to see an increase in MVP Points completed the best way would be to increase the size of the team. Please note that if you have a looming deadline then this option is not practical. If you have months of work remaining then it is.
- When your pm tries to do something outside of the Agile methodology your business practices you explain to the PM what they are doing, why it is a problem, and how to properly address their concerns within the methodology being used.