There was a sting in the tail of Mr Corbyn's questions: "When it comes to Brexit, this Government has delivered more delays and more cancellations than Northern rail".
"So, if we are serious about "protecting full access to the internal market of the EU" and ensuring "no new impediments to trade", logic dictates Labour MPs should be whipped to support the cross-party EEA amendment sent to us by the House of Lords".
United Kingdom proposals for a "backstop" arrangement to keep the Irish border open after Brexit are to be published "shortly", Downing Street has said.
Asked if he could stay in his job if the Government's backstop proposals did not have his explicit approval, Mr Davis said: "That's a question I think for the Prime Minister to be honest".
Britain's government will seek to overturn some amendments to its EU withdrawal bill to sever ties with the European Union when it returns to the House of Commons next Tuesday after suffering defeats in the upper house of parliament.
The latest round of official negotiations conclude on Friday, but it was unclear whether the document will be published when Mrs May's Brexit war cabinet meets on Thursday ahead of her departure for the G7 summit in Canada.
"Parliament should have the opportunity to debate and vote on it", he added.
Mr Corbyn can hardly be blamed for going on the number one problem facing Britain today and one on which Mrs May has proved time and time again, including yesterday, that she has few answers.
Meanwhile, Mrs May's decision to squeeze Commons consideration of the 15 Lords amendments to the EU Withdrawal Bill into a single 12-hour day on June 12 provoked an angry reaction on the opposition benches.
Mrs May also came under pressure from Tory MPs, with Crawley MP Henry Smith saying his constituents wanted her to get on with both Brexit and sorting out the rail mess.
Shadow Brexit secretary Sir Keir Starmer said EEA membership was too divisive in the Parliamentary Labour Party (PLP).
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The party is divided over whether to try and stay in the EU's single market.
Meanwhile, rebel MPs from both sides of the House of Commons are pushing for a Norway-style Brexit agreement which would keep the United Kingdom in the single market.
"I'm injecting some honesty about where we are in the Labour Party", he told BBC Radio 4′s Today programme.
Starmer said Labour MPs such as Chris Leslie and Chuka Umunna who backed the EEA amendment were well aware "it does not command support in their own party".
"This is one of those issues where if you just blindly follow orders people will not forgive you".
This includes votes on core Brexit issues such as whether Britain should leave the EU's single market.
At an Open Britain event, she said that Tories at all levels of government - including in the Cabinet - supported an EEA deal.
Brexit minister Suella Braverman said: "Labour have shattered their promise to respect the referendum result - this amendment means accepting free movement and continuing to follow European Union rules with absolutely no say in them, which is the worst of all worlds".
On the other side of the Commons at least 12 Conservatives have signalled their support for a future in the EEA in an amendment to the separate Trade Bill.
"That has got to change, we can not allow this culture of fear that has developed to continue any longer".