If by any chance it does go ahead, though, everything would hinge upon the format. McDonnell seemed to be hinting at a multi-option referendum, which presumably would include the May deal, remaining in the EU, and no-deal. But how would a three-option vote actually work? Nobody would ever seriously contemplate a first-past-the-post rule, because that would be like settling the constitutional future of the UK on a lottery (although of course that does beg the question of why we routinely choose governments that way). A bit more plausible would be a preferential voting system or a French-style run-off, which I suspect would be Remain's best realistic hope. But my guess is that we might instead end up with a two question format - the first question would ask whether the May deal should be approved, and the second question would give a straight choice between no-deal and Remain if the answer to the first question is "No". (The result on the second question would be voided if there was a majority 'Yes' on the first question.)
If you think it through, the dice would be loaded in favour of Brexit on that format. There would be extensive polling on both questions, and if the second question polling showed a clear majority for Remain (as you'd intuitively expect it to), Brexiteers would have every incentive to make a tactical switch in favour of campaigning for a Yes vote on the question about the May deal. With government, media, and Brexiteer support, the deal would in all likelihood be approved, and Britain would leave the EU as a result.
Incidentally, it's impossible to know whether there is already a natural majority in favour of the May deal without that sort of tactical switch. A Survation poll the other day showed a narrow majority in favour of the deal for the first time, but a new YouGov poll conducted at roughly the same time continues to show a massive majority against. That sort of difference can't be explained by the standard margin of error - either one firm is getting it completely wrong, or they both are. The YouGov poll also continues to show that Scotland is less supportive of the deal than any other part of Great Britain...
Support for the Brexit deal by region:
Rest of South: 29%
Midlands & Wales: 27%
North of England: 23%
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