First, give an evaluation of situation to your direct boss, provide her/him a time schedule you believe it is enough for you to finish, and ask her/his approval.
If your boss approves your proposal, just follow the schedule and finish the project.
If your boss does not approve the schedule, just directly let your boss know you need the time to do the job.
Do not put you in a situation without your own control.
Do the best is not good enough in this situation. You have to be specific and firm on your stand to get the job done.
