The EU is moving into full no-deal mode | The Guardian
It seems a new referendum is not in her book.
Can the British parliament vote down the brexit deal and then vote for no brexit at all or is that last decision exclusively on the plate of the cabinet in the UK?
A snap election in 2017 wasn't in her book until suddenly it was. Calling off the vote on the Withdrawal Agreement wasn't in her book until suddenly it was. So I don't think her ruling out a second referendum means it's not going to happen. This is all theatre, designed to show her backbenchers that she's done absolutely everything she can and it really, truely, is the case that the EU27 aren't going to budge.
At that point, the only way to resolve the problem is to leave with no deal (which I can't believe she'd allow to happen) or to accept this deal or to cancel A50 and remain. There's no way to get either this deal or cancel A50 through parliament at the moment. A general election won't help, and I think the only way forward is to cut the Gordian Knot with a second referendum.
I think, from her point of view, she wants to demonstrate she and her government did everything in their power to deliver the result of the first referendum but was nevertheless forced, very reluctantly, to put the withdrawal agreement to a second referendum so, if that referendum results in a conclusive "Remain" vote (which it almost certainly will, if the options are Remain vs Ratify, rather than Remain vs Leave on fantasy terms), she and her government can't be accused of sabotaging things in order to frustrate the will of the people, as expressed in the first referendum.
As to what parliament can do and what the cabinet have to do, the position is that, as a matter of EU and UK law, Britain leaves the EU, either with no deal or whatever deal has been agreed, on March 29, unless something happens to stop that. That "something" involves Parliament passing a new act to cancel (or suspend) the European Union (Withdrawal) Act, which would need Government support, and the PM either withdrawing the A50 notification unilaterally and permanently (very unlikely) or (far more likely) asking the EU to agree to extend the A50 deadline to give time for a referendum to be arranged.
So, parliament can vote the deal down, certainly, if it's given the chance to. But I don't see how it can prevent a "hard Brexit" if it does, unless not only the British government but also the EU27 agree to take steps to prevent a hard Brexit if it does vote down the deal.