Ben Bradshaw has predicted a "year-long" extension to Article 50.
When asked by talkRADIO's Julia Hartley-Brewer what he thought would happen in the wake of today's indicative votes, he said the country would "be looking at a longer extension", as proposed by the DUP yesterday.
"I still think there's a slim chance that the ERG, the Brexiteer tories, and the DUP could fold, and May's deal might go through. I think that's unlikely," he said.
"If that doesn't happen we're looking at a longer extension. A year-long extension that was proposed yesterday by the DUP, so we can try to work out as a country what the hell we want."
Today's votes will not be legally binding, and have come under fire from some who claim it is an attempt to overturn the Brexit vote.
However, Mr Bradshaw defended the move, arguing it was a chance for Parliament and the government to find common ground.
"We are where we are. Parliament and the government have not been able to agree on the type of Brexit and that's what MPs are trying to do today."