You'd have to accept May at her word that it is either her deal or No Deal. It's also a question of what in particular about the Deal you find unacceptable. If it's the backstop, ie if, under no circumstances, do you want to take out an insurance policy to protect the status of the Irish border in the absence of another solution, then perhaps there is nowhere else to go other than the three choices May keeps offering. If the UK were prepared to concede the principle of the Backstop, but focus on other aspects of the current agreement -- and there are, to be sure, a lot of points that are objectionable -- then they may yet meet with more flexibility from the EU.
It is perhaps a bit much to expect any more of an answer than that above, which is admittedly a bit of a cop-out*, but perhaps I'm arguing for a different approach altogether: namely, that the UK relax its position of exiting the EU "now", and focus on seeking to do it "sensibly". Maybe it still doesn't work, maybe there is nowhere to go if you want out other than to concede that there is no deal that can be reached that satisfies the UK and the EU at the same time. But I don't think that May's deal is the only and definitive test of this.
*Read: a massive cop-out.