What is that thing called where you only need to survive or cope with an exigent circumstance for a short time like 10-30 days?

In addition to "Survival Mode" I've also heard this called "Crisis Management". Not sure if that's what you were looking for.

I guess "abide" (to bear patiently) and "endure" (to remain firm under suffering or misfortune without yielding) would both work, though neither has an inherent notion of time.

This to shall pass, a grind?

I would call it an ordeal

grit your teeth / grit those teeth comes to mind.

although it doesn't have to be short in terms of time, just temporarily.

also the old timey gird up your loins