In Imrei Pinchas (Mikeitz 75), a compilation of teachings from the great Rabbi Pinchas of Koritz, zy”a, are brought down. We find that he brings down the chiddush just mentioned in the name of the Sifsei Kohen; but he adds a wonderful and valuable message. When a Jew is standing near a mezuzah, with the name שד"י inscribed on it, he should follow the example of the shevatim. He should have in mind the tefilah uttered by Yaakov Avinu: “May Kel Shakkai grant you mercy” with the implication explained by Rashi: He Who said to the world “enough!” should say “enough!” to my troubles.
We can now add another tantalizing tidbit. When Yaakov uttered this tefilah, he felt that “midas hadin” was hovering over him and was the reason that he had been subjected to all of the troubles mentioned above. To add to those troubles, he was now being asked to send his youngest son, Binyamin, to Mitzrayim. Therefore, in an effort to mitigate and sweeten the forces of “din,” he invoked the name ישרא"ל which can be formed with the first letters of the words: א'ל ש'די י'תן ל'כם ר'חמים.
Furthermore, we can suggest that Yaakov Avinu chose to sweeten the forces of “din” specifically by invoking the name Yisrael as a preparation to sweeten the forces of “din” for all of his descendants throughout the generations who are called the people of Yisrael. Therefore, when a Jew stands next to a mezuzah with the name שד"י written on it, it is an opportune time to have in mind the tefilah of Yaakov Avinu: "ואל שדי יתן לכם רחמים". He invoked the name ישרא"ל to mitigate the “din” every Jew is subjected to and the name שד"י to put an end to our troubles; in the words of Rashi: He Who said to the world “enough!” should say “enough!” to my troubles.
