Often used figuratively to suggest doing something is possible with extra effort or in a tight situation. We can finish the project today, at a push.
Pro Tip 2/3
Casual Tone
'At a push' is typically used in informal conversations rather than formal or written English. I could binge-watch the entire season tonight, at a push.
Pro Tip 3/3
Subtle Nuance
The phrase implies a reluctance or acknowledgment of difficulty; it's not the preferred option. We could hike to the peak at a push, but it might be risky.