הֵ֣ן אִיתַ֗י אֱלָהַ֙נָא֙ דִּֽי־אֲנַ֣חְנָא פָֽלְחִ֔ין יָכִ֖ל לְשֵׁיזָבוּתַ֑נָא מִן־אַתּ֨וּן נוּרָ֧א יָקִֽדְתָּ֛א וּמִן־יְדָ֥ךְ מַלְכָּ֖א יְשֵׁיזִֽב׃
Narito, ang aming Diyos na aming pinaglilingkuran ay may kakayahang iligtas kami mula sa nagliliyab na hurno ng apoy; at mula sa iyong kamay, O hari, ay ililigtas Niya kami.
Sefer Daniel; Opportunity in Exile
We believe that the Midrash is teaching that our great trio is well aware of the parallels between the situations. Chananiah, Mishael, and Azariah draw the courage and inspiration to enter the fire. The memory of the miraculous rescue of Avraham Avinu gives them the courage to tell Nevuchadneztar (Daniel 3:17) that Hashem has the power to rescue them from the fiery flames.
Ibn Ezra
[Daniel 3:16] Shadrach, Meshach, and Abed-nego answered (עֲנוֹ - ʿAno): We have no need (לָֽא־חַשְׁחִין - la chashchin): [This means] We do not need (lo tzrichin anu) to answer you [in this matter]. Because our God whom we serve (עובדים - ovdim), acting powerfully (lit. 'like one who cleaves [or plows] and breaks through' - כמו פולח ובוקע) upon the earth, is able to save us from the fiery furnace. Also [He is able to save us] from your hand, if He wishes. And behold, if He does not save [us]... it shall be known to you [i.e., their resolve remains unchanged, as elaborated in v. 17-18].