In English, the general metaphor is that we move (and "now", the current time, moves) forward through time, while deadlines (and other specific dates) are fixed. We often use travelling (walking, or riding in a car) as a metaphor for time.
So it is natural to say "we are approaching the deadline", "we are getting close to the deadline", "we are near the deadline", or "there is a deadline coming up". Whether other phrases work or not depends on whether they work with the "riding in a car" metaphor.
- An intersection is approaching.
- An intersection is getting near.
- An intersection is coming closer.
- The deadline is approaching.
- The deadline is getting near.
- The deadline is coming closer.