Government's Parliament Majority
It's hazardous for the representatives in a representative democracy to openly defy the will of the electorate, so some grounds is needed to make it appear one has not done so. I could maybe see a new referendum being held at some point, which would potentially allow politicians on both sides to avoid taking personal responsibility for the decision. Like impeaching Donald Trump, it's a very tricky business that, if it's to stick, would have to be gradually sidled up to, not making any sudden moves that might leave behind part of the needed coalition as one coaxes it to follow along. It can be really hard to judge where one is along that sort of curve; to some extent, reaching a point on the curve becomes a matter of successfully projecting confidence that one has reached it, so the judgement of reaching it is not separable from the act.
A new referendum might actually be best. A lot of young people didn't vote because they thought it didn't matter. There's some evidence that the majority of the British population didn't want Brexit, but not enough to override an actual vote (I wouldn't see that as justified in the face of anything short of criminal tampering with the election, hard proof that the results cannot be trusted; here, no one's doubting that the votes of people who bothered to vote were counted accurately). "Let's vote again" seems the simplest and most direct way to deal with that. If the deal falls through, they would have sufficient impetus to call for one.