There's a good idea here, to manage your level of commitment, but it's lost in the idea that it's a binary decision.
To get high performance without burnout it is necessary to switch from complete engagement to complete disengagement every few hours.
The Serenity Prayer from Alcoholics Anonymous is asking for the right thing here, even if you aren't religious.
"God grant me the serenity to accept the things I cannot change; courage to change the things I can; and wisdom to know the difference."
It's great to be passionate but it's also important to be detached about things you can't control.
One detail that is missing from this story is the nature of the deadline. Lateness is endemic in software development, and successful projects often get delivered years after they were promised. Late doesn't necessarily mean "failed."
You can't go wrong learning more about project management so you can have a more correct understanding of the situation.
Whatever you do, keep your honor. Being ambiguous about wanting the job gives you the unique freedom to refuse any order that you truly don't want to carry out.