What did the magicians mean when they declared "Etzba Elokim Hi!"?
Rashi and Ramban #1: They conceded that it was not Ma'aseh Keshafim but a Divine act.
Ramban #2 (citing the Ibn Ezra) 1 : They meant that it was a natural phenomenon, brought about by Elokim (in whom Par'oh believed) but not by Hashem (the G-d of Yisrael (in whom he did not).
Rashbam: They meant that it must have been a natural phenomenon that had nothing to do with Moshe and Aharon. 2
Sanhedrin 67b #1: We see from here that witchcraft cannot produce anything smaller than a barley-grain.
Sanhedrin, 67b #2: Witchcraft can produce any size objects, but it cannot gather those that are smaller than a barley to one place. 3
See Ramban, who cites a number of proofs that 'Etzba Elokim' and similar expressions refer to acts attributed to Divine Providence. Moreover, the fact that Par'oh no longer called the magicians to appear before Moshe indicates that they submitted to his superiority. Refer to 9:11:1:1.
Rashbam: Because, seeing as they insisted on believing that Moshe and Aharon were magicians, if they were able to produce lice then there was no reason why they should not also have been able to do so.
See Torah Temimah note 4.
Why did they refer to "Etzba Elokim" and not "Yad Hashem"?
Rashi (in Rus 1:13): Because the term "Yad Hashem", is confined to the plague of pestilence.
Ramban: They meant that this was a relatively small miracle on Hashem's part, and they mentioned the Name Elokim because among themselves, they never used the Name Havayah, only when they spoke to Moshe, since that was the Name with which Moshe addressed them.
Moshav Zekenim: Hashem caused them to say 'Etzba', to teach us that Keri'as Yam Suf, which was through Hashem's "Yad", was five times as severe as all the Makos. 1
As is stated in the Hagadah.