What did Hashem mean when He said "ve'Atah Hanichah Li"? Was Moshe holding on to Him?
Rashi: He was insinuating that, if Moshe would intervene on behalf of Yisrael and Daven for them, He would not destroy them.
Ramban, Targum Onkelos and Targum Yonasan: Hashem meant that Moshe should let Him destroy Yisrael in His anger and not Daven to stop Him. 1
B'rachos, 32a: Moshe did indeed take hold of Hashem (Kevayachol), 2 like a person takes hold of his friend's garment, and declares 'I won't leave You until You pardon them!'
How did Hashem intend to destroy Yisrael?
Ramban (according to Kabalah): He would leave His Midas Rachamim aside, and allow His Midas ha'Din to destroy Yisrael. 1
Rosh (in Pasuk 7): Through the five damaging angels that descended - Af, Ketzef, Cheimah, Hashmed and Mashchis. 2
Ramban: Hence in Pasuk 11, Moshe Davened to "P'nei Hashem Elokav" (the Midas ha'Din, since Hashem had discarded the Midas Rachamim.
Rosh, Ibid.: Moshe then mentioned the three Avos, and the last three departed. Moshe asked Hashem to stand in front of (block) Af ("Kumah Hashem be'Apecha" - Tehilim, 7:7), whilst he himself stood in front of Cheimah ("Lulei Moshe... Lehashiv Chamaso" - Tehilim 106:23), and the Gemara in Nedarim, 32a states that Moshe killed Cheimah.