gut it out

gut it out AND tough it out (to continue with the task at hand even though it may be painful or difficult; show pluck and perseverance in the face of opposition or adversity) — перебарывать себя, пересивать, преодолевать себя, ...

It's probably related to phrases like "no guts, no glory," and others that use "guts" as a colorful synonym for courage, perseverance, and physical toughness.

Example: I know it's hard but we'll just have to gut it out. (dictionary.reference.com)

Example: His boss has a terrible temper, but Joe is determined to tough it out . (dictionary.reference.com)

Related vocabulary:
[bite the bullet]
[suck it up]
[needs must]