Explanation:

- We're asking them to increase the deadline: This implies making the deadline larger, which doesn't quite fit in context. We usually increase time or quantity, not deadlines.

- We're asking them to enlarge the deadline: This option suggests a physical size change, which is not applicable here as deadlines are not physical objects.

- We're asking them to broaden the deadline: This implies making the scope wider, similar to enlarge, and is also not suitable for deadlines.

- We're asking them to extend the deadline: This means to push the deadline further out in time, which perfectly fits the context of prolonging a deadline.