It means "if absolutely necessary" or "if it comes to the crunch."

अगर बहुत जरूरी हो

English Usage: "We might be able to finish the project by Friday, at a push."

Hindi Usage: "हम शायद शुक्रवार तक प्रोजेक्ट को खत्म कर सकते हैं, अगर बहुत जरूरी हो।"