The Talmud notes that when Daniel said in his prayer:1 "and let Your countenance shine... for the L-rd's (Adnay) sake," he meant to invoke the merit of Avraham, who called G-d "the L-rd."
Daniel, who lived during a time of exile, asked for the revelation of the "One Eye of Atika Kadisha" the level at which "the Guardian of Israel neither slumbers nor sleeps." He asked that his request be granted in the merit of Avraham, who called G-d, "the L-rd."
Daniel did not say "for Your sake," for the term "Your" refers to a flow from the essence which G-d Himself brings forth. Rather he said "for the sake of Adnay," [similar] to Avraham, who called G-d Adnay. Though Adnay too involves a flow from the Essence, it is drawn down through the spiritual service of total self-sacrifice.
Daniel's prayer was unlike Moshe's. Moshe prayed that G-dliness be revealed within the Jewish people, and through them to the rest of the world. This is indicated by the verse:2 "And you shall make for Me a Sanctuary, and I shall dwell amongst you," concerning which our Sages comment:3 "The verse does not state 'I will dwell in it,' but 'amongst you' an indwelling within each and every Jew."
Daniel prayed that the essential flow of G-dliness be revealed [not only internally, but] externally as well that there be an actual revealed manifestation of G-dliness an indication of which would be the rebuilding of the Holy Temple. Daniel also prayed that this level be revealed within the "miniature Holy Temple"4 found in every Jew, and that all hindrances to Torah study and Divine service be removed.
Daniel beseeched G-d that his prayers be answered in Avraham's merit, for Avraham possessed merits that even Moshe lacked [in that he made G-dliness known to a world which knew nothing of Him]. Though Moshe too lived during a time of exile, an awareness of G-dliness existed in his time. Even during the days of Yosef, Pharaoh was aware of G-d, for Yosef often mentioned the Divine name Elokim.
During the time of Avraham, however, people neither knew nor cared to know about G-dliness. Concerning this period, the Midrash tells us:5 "Until Avraham, the world was in a state of darkness; when Avraham came, it began to become light." Avraham's total dedication and self-sacrifice in making G-dliness known lifted him to the highest of levels.
This then is what the Talmud means by the statement: "Even Daniel was answered only in the merit of Avraham." Daniel too lived during a period of exile, and prayed with total self-sacrifice, so it would seem proper that Daniel be answered in his own right. Yet he was answered in the merit of Avraham since Avraham was the first to display total self-sacrifice for G-dliness. As the "trailblazer,"6 Avraham made it possible for others to follow.
This too was implied by Daniel when he said:7 "And now, our G-d, hearken to the prayer of Your servant...." The word "now" has a twofold meaning. "Now," during exile, is an especially appropriate time for prayers to be answered. In times of exile, Jews are downtrodden and lack spiritual acuity; spiritual service is so difficult that even a minor service is a great achievement.
"Now" also refers to the service of teshuvah (repentance).8 Teshuvah implies that "the now" the present, is not the same as the past, and that there has been a change for the better. For this reason, it is appropriate to ask that G-d "hearken to the prayer of Your servant, and to his supplications."
Daniel, the only person entrusted by G-d with the secret of when the exile will end, prays that He accept the teshuvah of the Jewish people, and that He hearken to our prayers and supplications and redeem us with a complete redemption through the righteous Moshiach.
In summary: Avraham, the first person to totally sacrifice himself for G-dliness, merited to draw down a flow from the Divine Essence. Daniel foresaw the tribulations during these latter days of exile, and prayed that G-d accept the teshuvah of the Jewish people and send our righteous Moshiach.