what can be accomplished in a week

This idea is relevant to aseres ymei teshuvah, but what can I do -- the idea only came up here in parshas Noach.
     
Subtract Rosh haShana and Yom Kippur and aseres ymei teshuvah amounts to one week.  One week to correct a year, a lifetime's work of mistakes!  How is that possible?
     
Rashi observes that at the beginning of the parsha Noach is called a "tzadik tamim," yet when Hashem appears to Noach to tell him to enter the ark he tells him that "oscha ra'isi tzadik lifanei," he is a tzadik -- Hashem leaves out the word "tamim."
     
Ksav Sofer offers an original explanation (see Rashi for a different explanation) for the discrepancy: Rashi writes that Hashem delayed the command to enter the ark until the after the seven days of mourning for Mesushelach were completed.  Mesushelach was a tzadik, so long as he was alive, the flood was held off.  Ksav Sofer adds that so long as Mesushelach was alive, Noach was also not held accountable for failing to rebuke the people or for failing to daven on their behalf.  Why should he have that responsibility when there was a tzadik like Mesushelach around?  However, once Mesushelach died, the world rested on Noach's shoulders.  Since Noach at that point still remained passive and did nothing, some of the shine of his tzidkus was lost.  He was no longer a "tzadik tamim," but merely a "tzadik."
     
Mesushelach lived 969 years -- he literally had hundreds of years to try to make an impression on the people around him, to arouse them to teshuvah.  When he died, Noach had one week to step in and fill his shoes before the flood hit.  Imagine a shul where the Rabbi has held the pulpit for decades and has not made a dent in raising the religious observance of the community, not for lack of effort, but for lack of a receptive audience.  The Rabbi passes away, and the assistant Rabbi must now step in.  Are you going to hold the assistant accountable for failing to reach the community mamesh during the week of shiva of his predecessor when his predecessor couldn't reach them in the decades he served?!  Here too, what kind of knock it is on Noach's tzidkus when he couldn't do anything in only a week when Mesushelach was no more successful in centuries?!
     
Yet the Torah doesn't see things that way.  Who knows what you can accomplish is a week of dedicated effort?  Remember, Hashem would have saved Sdom had there only been a minyan of tzadikim there.  Noach didn't have to reach the entire world -- he could have focused on one, on a handful, of people and that might have tilted the balance to prevent the flood.