Talmidei Rabbeinu Yonah [Brachos 49] write that the kedusha of the Jewish people is predicated on the kedusha of Shabbos. That is what we mean when we say in the bracha מקדש השבת וישראל והזמנים.
What is the root of this connection?
וכרות עמו הברית. Hashem was "kores bris" with Avraham. Kores means to "cut off" [as in the word "kares"] while "bris" - covenant, brings people together. So how is one "kores bris" which seems to be an internal contradiction??
The answer is that a bris by defintion cuts everyone else off. When one gets married and creates a bris with his/her spouse this effectively cuts everyone else off from this special union. Hashem was never "kores bris" with the goyim becasue he doesn't have an exclusive relationship with them. But with klal yisrael Hashem enjoys an exclusive bond. Only with us Hashem was kores bris.
After the mabul it says יום ולילה לא ישבותו which means that goyim are obligated to work seven days a week and are not allowed to keep Shabbos. When we received the mitzva of Shabbos, we were cut off from all of the nations and sealed our level of holiness and exclusive relationship with Hashem. יום ולילה לא ישבותו doesn't apply to us.
This explains why our kedusha is predicated on the kedusha of Shabbos.
[Maran HaRav Hutner Shavuos 1972]
Based on this we can explain what we say every Shabbos in davening. "ושני לוחות אבנים הוריד בידו וכתוב בהם שמירת שבת". Moshe brought down the two tablets of stone upon which were inscribed the mitzva of keeping Shabbos. This is difficult because there were ten mitvos on the tablets, not just Shabbos??
However, based on the foregoing we understand that Shabbos more than any other mitzva symbolizes the kedusha of klal yisrael and that is why it is singled out.
That also might be why a mechalel shabbos has the status of a goy for many halachos [such as his wine that he touched being forbidden to drink]. He has effectively lost his kedushas yisroel.
I have a chiddush li-halacha based on this but MAYBE another time.
:-)