能力（キャパシティ）の限界ぎりぎりでやっている（がんばっている）

work at the limits of one's capacity
フレーズ

The Spanish government has warned that intensive care units around the country are working at the limits of their capacity, and that the pressure on them will continue to be enormous even when the number of new cases peaks.
https://www.theguardian.com/world/live/2020/mar/30...