"If we don't want no-deal, and we don't want the Prime Minister's deal, what are we going to do to resolve this?"
Hancock said the pharmaceutical industry was doing everything it could to prevent shortages of medicines resulting from any delays at borders resulting from a no-deal Brexit.
Mr Coveney said the backstop was crucial in preventing a hard border.
Speaking to Ian Payne, Tory MP Dominic Grieve said that it was "quite clear" that MPs do not support leaving with no-deal and instead would be prepared to stop Brexit if they had to decide between the two.
Coveney said, 'Even in a no-deal Brexit situation every party and every MP in the United Kingdom will have a responsibility to ensure there is no return to a hard border and Northern Ireland is protected.
"That is not about blocking Brexit, that is about being responsible and making sure you can get a Brexit deal". One Tuesday night, in a series of votes on parliamentary amendments, they will set out what they want her to do next.
US Sees Little Chance To Save INF Treaty Days Before Deadline
Russian President Vladimir Putin has threatened to develop nuclear missiles banned under the INF treaty if it is scrapped. The INF has been the backbone of Europe's security system, curbing the risk of nuclear attack.
The Police Service of Northern Ireland has been given extra resources for Brexit but says it hopes it can adopt a softer community-style approach.
Sir Graham, who is chairman of the highly influential 1922 Committee of backbench Tory MPs, told the BBC: 'My amendment is an attempt to bring the kind of compromise forward that can actually attract the support of a majority of the House of Commons. But Coveney's comments seemed meant to close down the prospect of the backstop being renegotiated.
But Education Secretary Damian Hinds said alternatives to the controversial Northern Irish backstop were already being considered.
The government is set to consult Parliament on what extra hours will be needed in order to get the necessary Brexit legislation onto the statute book before the UK's planned departure from the European Union at 23:00 GMT on 29 March. Responding to reports that MPs could be asked to sit for 12-hour days, instead of the normal eight-hour days, and to sit on Fridays and through the whole of February, a Downing Street spokesperson said: "We remain committed to ensuring all necessary legislation is in place for exit day on 29 March, and it important to stress we are confident of meeting that commitment".
She said MPs would have a chance to debate and vote on any decision, adding that the government recognised the need to balance their constituency and family responsibilities.