Poor wording. Given the high degree of polarization it's expectable that hardline Leavers would prefer a vote b/w "no deal" and Chaqeurs while Remainer b/w Chaqeurs and Remain. They'd hold a ref w/ three options but it's unlikely anybody had this in mind while being surveyed. /1
In any case it is not clear if either option would be acceptable for majority of people to be held. Probably the best option to go forward is a three way either in two rounds or w/ AV. However, it is very likely that in any way electorate will feel betrayed. /2
Nobody likes Chaqeurs and EU is unlikely to accept it, why should they? They know about their strengths and they aren't desperate for a deal. If Remain or no deal wins there would be ongoing opposition. /3
It's not even clear whether UK could stand no deal, politically, economically & security wise. Chance is good UK'd be soon back on the table in a weaker position which will cause further grievance. Surely, not a problem for EU but UK's political sys seems not fit for purpose. 4/4
