Mrs May was speaking after a five-hour Cabinet meeting at Downing Street had ran over into a seventh hour.
In a Tweet following the statement, EU Council President Donald Tusk called for patience.
And Mr Hinds believes it's bar far the best option on the table.
The politician appeared on the Mike Graham show following last night's series of "indicative votes", in which MPs failed to find a majority for any alternative Brexit options to the Prime Minister's deal.
"I know there are some who are so fed up with delay and endless arguments that they would like to leave with no deal next week, I've always been clear that we could make a success of no deal in the long term".
The BBC's John Pienaar said Prime Minister Theresa May's cabinet had considered plans to "ramp up" no-deal Brexit preparations and a snap general election had also been discussed.
French President Emmanuel Macron and Irish Taoiseach Leo Varadkar are meeting in Paris to discuss the impact of Brexit.
A no-deal Brexit was "never our desired or intended scenario" but "becomes day after day more likely", he said.
A group of cross-party MPs are putting forward a new short bill created to prevent the United Kingdom from leaving the European Union without a deal on 12th April.
President Macron told reporters that the European Union "cannot be hostage to the political crisis in the UK", and the government must come forward with "credible" reasons for an extension.
Speaking in Brussels, Mr Barnier said: "An extension would carry significant risks for the EU".
The group behind the bill, which also includes former Tory chair Dame Caroline Spelman, Commons Brexit Committee chair Hilary Benn, former attorney general Dominic Grieve and Liberal Democrat Norman Lamb, hopes once it has passed the Commons it could be approved by the House of Lords and granted Royal Assent in time for the emergency European Union summit on April 10.
The PM said: "This is a hard time for everyone". The Prime Minister has a responsibility to prevent that happening. Letwin admitted that the bill would be "difficult" to pass, saying, "This is a last-ditch attempt to prevent our country being exposed to the risks inherent in a no-deal exit".
A cross-group of parliamentarians, including Conservative Sir Oliver Letwin and Labour's Yvette Cooper, will on Wednesday bring forward a bill instructing the Prime Minister to request an extension to the negotiating time beyond 12 April. "But it is definitely worth trying", he added.