Any single word to denote the maximum possible deadline

I am not a native English speaker. So my explanation might not be clear. Still I will try to explain. Please forgive my bad English.

When I was writing an email, I want to convey this meaning:

"We can plan to complete this by Monday or if in case it is not completed on Monday(which is not desirable, but can be tolerated in a worst case scenario. But it is a must that it should be completed on Tuesday), then the maximum time we can wait for the completion of the task is Tuesday".

How I can write this concisely and in a less complicated way. Something such as:

We can plan to complete this by Monday or ----- by Tuesday.

Is there a single word that I can use to fill in the blanks, that will convey the meaning that the task must not be extended after Tuesday? I thought the word lately will fit there, but it has somewhat opposite meaning.

drop-dead date

Used in contract law and in publishing. In law it is the date by which something must be done to avoid adverse consequences, such as seizure of property.

Its use in book and magazine publishing refers to the time text must be in hand in order to make it into the book, magazine, or newspaper.

In computer programs, revisions or alterations in code are necessary by a drop-dead date if they are to make it into a particular release.

Definition of drop-dead date US : a date by which something must be done or finished : a deadline that must be met They were given a drop-dead date of June 30 to accept or reject the contract.

(Merriam-Webster) https://www.merriam-webster.com/dictionary/drop-dead%20date

One often sees the idiom no/not later than used to convey your "maximum possible deadline". From M-W:

no/not later than: by (a specified time) : at, in, on, or before (a specified time); e.g., "We'll need to know your decision no/not later than next week."

Your example (edited slightly):

We can plan to complete this (project) by Monday, but we will complete it by no later than Tuesday.

One often sees the related acronym NLT. For example:

You must complete this (project) by NLT close of business Tuesday.

One also sees the term hard deadline used to convey your "maximum possible deadline". From M-W:

hard: firm, definite; e.g., reached a hard agreement

Example:

Close of business Tuesday is a hard deadline

A hard deadline -- in contrast to soft deadline --is one that must be met, that is not subject to change, that is firm.