It is quite well established that BREXIT is the "middle class" versus the "working class", if you go by the Guardian the working classes are currently unhappy with a labour party which they consider to have been hijacked by the upper middle class which no longer represents their interests.
Love him or hate him, Jeremy Corbyn held the most sensible nuanced approach towards the EU that a Labour leader with an ounce self preservation and electoral awareness could take. If he'd have come out more in favour of the EU he'd have pissed off more of the Labour traditional vote base, who are increasingly not voting Labour. Mrs May has been doing a spot of electoral repositioning with the conservative party, who stand to take the traditional labour vote. (see the last conservative party speeches)
If Labour blocked the BREXIT vote, then it is likely that the conservatives are going to take once in a century opportunity to brand Labour with the "nasty party" label, and people are going to believe it. The working class who voted to leave the EU in the referendum are quite likely to cease voting for Labour en masse, leading to permanent electoral oblivion for Labour.
Bridges have already been burnt with the EU, the remains have been dynamited and the remaining fragments have been taken away to be reused for charcoal. If we did stay in the EU at this point then we have no friends and no influence. Frankly, I think that both the UK and EU would be better off leaving and staying on acceptably good terms.
And on that note, good terms will not be obtained by telling the EU that we will have a vote on their offered terms, and if they are sufficiently bad then we will consider remaining within the EU. Anybody suggesting doing this is an idiot. It will simply lead to a set of awful terms being offered and one of the following will happen:-
1) A Phyrric victory. We vote to remain in the EU on the basis of a toxic brew of fear and hate. relations with the EU are forever fucked beyond any potential possibility of repair as UK popular opinion becomes steadily more xenophobic. In addition, Labour's traditional voting base who voted to leave the EU at the referendum defect to the conservatives when Labour people openly celebrate. There is shock at the next (and following) general elections when the traditional labour vote fucks off elseware, and Labour becomes a smaller party than the Lib Dems. Possibly (hopefully not) the Marxist hippies at the Guardian get the class war they have been calling for since forever, but are confused when they realise that the class war is aimed squarely at them.
or; 2) We vote to leave, despite horribly harsh terms offered causing serious damage to Great Britain PLC. Labour is still electorally exterminated by the working class leaving a perpetual conservative majority, with the self inflicted damage to jobs and their prospects near certainly blamed on the "remoaners", and relations between the EU and UK basically stay at a level that would reasonably be described as "undeclared war".
Surely just accepting that people want to leave the EU and getting the best possible result is the most sane and least damaging course of action, from the basis of economics, domestic politics and international politics?