Yes, he won't, he's sure in his mind that he can make this go away if he says sorry, and he says sorry like a kid forced by his parents, and in saying it he believes the slate is wiped clean for him to carry on lying, as he has consistently done since he appeared. The man is a moral vacuum.
But 14 ministers resigning in a single day is a record, 38 ministers and aides in total, so watch this space.
Edit; 41 now and he sacked Gove, probably a move to make him seem human, or just for kicks, who wouldn't sack Gove, I can imagine the only reason to give him a job is so you can then sack him, just to see that blubbery face drop, and then say, kidding, yeah, no you're sacked.