get through

It's actually rather straight forward (all puns intended and copyrighted). To get through means to pass through a period of time without suffering harm.

This sentence implies that unless the remedy recommended (but not stated in the sentence, as the context is lacking) is used, then in the course of one week, one would put oneself into danger (jeopardize) in regard to the hearings which will be held the following week.

If you could post a more complete quoted text, it might be easier to explain.

To "get through" a period of time does not always mean to pass through it without suffering harm, although that is probably what the phrase means in the quoted passage. It can just mean to endure whatever happens during that period.

thank you very much.. It helps a lot