The Normanton, Pontefract and Castleford MP’s claim came amid cabinet divisions over a no-deal Brexit breaking to the surface again as the Prime Minister faced a major Commons clash on the issue.
The House of Commons will vote on the latest Brexit bill on Tuesday, and Ms Cooper’s amendment would guarantee parliamentary time for a private members’ bill that would extend article 50 to the end of 2019 in the event Mrs May failed to secure a deal by late February.
Speaking to Andrew Marr on the BBC, Ms Cooper said that somebody needed to “take responsibility” and said the move was not about blocking Brexit.
During the interview, Mr Marr said that her amendment depended upon the support of Labour leader Jeremy Corbyn.
Ms Cooper said “I hope that he will support it,” adding: “I suppose what I would say to him, to the Prime Minister, to government ministers – which I think also want to make sure that we don’t have no deal – is in the end we cannot, and the Prime Minister cannot do this, we cannot keep waiting for other people to sort this out.
“We cannot just carry on with a kind of game of chicken that you [Mr Marr] described.
“That’s not a way to make sensible decisions.
“You need common sense, actually in the end somebody needs to take responsibility and say ‘If the Prime Minister runs out of time, she may need some more time’, and that is not about blocking Brexit, that is about being responsible and making sure you can try and get a better deal.”
Meanwhile, Education Secretary Damian Hinds insisted he could not envisage a no-deal Brexit being Government policy.
The comments came after Leader of the Commons Andrea Leadsom branded attempts by MPs to kill no deal as an option, through a series of Commons amendments on Tuesday, as a “thinly veiled attempt to stop Brexit”.
Mr Hinds told Sky News’s Sophy Ridge on Sunday: “I don’t envisage no deal becoming Government policy. We want to avoid a no deal. No deal would not be a good outcome.”
Mr Hinds insisted there were advantages to the controversial backstop proposals intended to avoid a hard border in Ireland by getting the UK to obey EU customs rules if no wider trade deal is agreed after a transition period. The Education Secretary said: “There are multiple reasons to believe the backstop would never come into place.
“And, even if it did, actually there are some advantages to the backstop as well as drawbacks.”
Irish foreign minister Simon Coveney said the EU was committed to a backstop.
He told BBC One’s Andrew Marr Show: “The European Parliament will not ratify a Withdrawal Agreement that doesn’t have a backstop in it. It’s as simple as that.
“The backstop is already a compromise. It is a series of compromises. It was designed around British red lines.
“Ireland has the same position as the European Union now, I think, when we say that the backstop as part of the Withdrawal Agreement is part of a balanced package that isn’t going to change.”
Health Secretary Matt Hancock denied Mr Coveney’s comments meant Mrs May’s Brexit deal was “dead in the water”.
“Not at all,” said Mr Hancock. “That’s a negotiating position the Irish are taking, but I think it’s also extremely clear from that interview and the tone... Ireland doesn’t want to have a no-deal Brexit. The whole purpose of the backstop is to avoid a hard border, which risks being a consequence of a no-deal Brexit.
“The idea the EU and the Irish Government would drive this process to a no-deal exit in order to try to achieve something which is intended to avoid no-deal Brexit, that is not going to happen.”
However, Brexiteer Tory MP Andrea Jenkyns said she wanted the PM to abandon the backstop, saying: “I’d like to see her bin the backstop. I think we need to bin it completely.”
The comments came as it emerged preparations are being looked at for the possible imposition of martial law after a no-deal Brexit.