New deal - There's no one to negotiate with
No deal - Parliament will block it
May's deal - No. Not after he voted it down
No Brexit - is what's going to happen because nothing else can
You can't just leave right now by royal command or something. Even with "no deal" we still can't leave until November.
And his government - MINORITY government - would not survive that long.
Europe says no new deal, and he just brought Theresa May's down to stop her deal. he would never get away with it. No with parliament, his party or the country.
So that leaves no Brexit.
And like you also said, that is a resignation, especially since he made Theresa May resign for exactly the same thing.
And that's why we're about to get a general election.