There were three possibilities from a simplistic viewpoint:
1) Remain and keep status quo
2) Leave (with no deal if necessary) for better or worse
3) Leave, in the believe that UK will be better off with new deals
Parliament has voted against no deal. To be fair to to them, opinion polls indicate that the majority of population don't want no deal either. So realistically, "no deal" will probably now need to win a second referendum if it is going to happen. Category 2 Leavers (quite understandably won't like this one bit and feel cheated) but this look like the reality now.
Not many believe UK will be better off with leaving with May's deal. Yes, one can say that she negotiated badly, was incompetent etc etc but this doesn't change the fact that EU is not going to give us a better deal now or in two years time. It is very possible that a percentage of Leave voters in category 3 don't want Brexit if it means May's deal.
And if we were to give up Brexit, many of the Leavers will be understanding very upset and there will be political and social chaos for years to come.
Hence the mess we are in.
The government and parliament are in a no-win situation and this will drag on. Hence, however unpalatable a second referendum is in principle, it is a way out of this deadlock and give some "sort" of legitimacy to the final decision made.