The mishna/gemara talks about a situation in which a person finds himself far away from civilization, such as lost in the desert, and does not know which day it is. The question being, how does the person know on which day to observe Shabbos, if he does not know what day it currently is? Depending on the exact situation, the answer given is that such a person would simply choose a day and observe Shabbos on that day and count the rest of the week around that day - until he finds his way back to civilization and finds out what day it actually is.

That might be fine for observing Shabbos in the desert, but don't expect to use it to get out of work on Tuesday. In Louisiana there was a lawsuit about religious discrimination. A school teacher was suing after her demand to give her off on every Tuesday from 10 Am until Wednesday 10 AM to observe her Sabbath was rejected. Had she been lost in the desert, maybe her claim could have worked, but in the heart of Louisiana they did not take so kindly to the idea.

The court actually rejected her claim and allowed the school to fire the teacher. Not because she has not right to make up her own Sabbath, and not because she was crazy, but because the legal accommodation for religious beliefs must only be insisted upon when it does not significantly impose too much of a burden the employer. A schoolteacher who must teach on the weekdays, and the continuity of the teaching is important for building a relationship with the students, observing Sabbath on Tuesday is too much of a burden on the employer.


And, to conclude, that reminds me of the joke of the three hassidim:
Three Hasidim are each talking about who has the greatest Rebbe: 

The first one says: "Our Rebbe is so great, we were walking home from schul on Shabbos and it was very hot. We said Rebbe it is so hot what can we do?" The Rebbe stopped and he prayed. And in front of the Rebbe and behind the Rebbe there was heat. And to the right of the Rebbe and to the left of the Rebbe there was heat. And in the area around the Rebbe it became cool and fresh and they all walked home. 

The second one says: "That's nothing! We were walking home from schul one Shabbos and it started to rain really hard. And we said Rebbe, we're going to get sick what should we do?" The Rebbe stopped and he prayed. And in front of the Rebbe and behind the Rebbe there was rain. And to the right of the Rebbe and to the left of the Rebbe there was rain. But in the area around the Rebbe, there was no rain, and they all walked home. 

The third said, "Is that all??" We were walking home from schul on Shabbos, and we spotted a large bag filled with gold coins that was lying in the street. And we said Rebbe, so much money, we could do so much work for the Hasidim, what should we do??" And the Rebbe stopped and he prayed. And in front of the Rebbe and behind the Rebbe there was Shabbos...