Work and Pensions Secretary, Amber Rudd, has said history will take "a dim view" of ministers if the UK leaves the EU without an agreement.
Ms Rudd told a cabinet meeting earlier that the UK would be less safe if there was a no-deal Brexit.
Business Secretary Greg Clark has also told MPs a no-deal exit in March "should not be contemplated".
MPs are set to vote soon on a measure which may restrict the government's tax powers in the event of a no-deal exit.
The government has refused to rule out leaving the EU without an agreement and is continuing to make contingency plans.
Transport Secretary Chris Grayling told the Commons that ministers would be accused of "irresponsibility" if they weren't planning for all eventualities.
In other Brexit developments:
- Brexit Secretary Stephen Barclay has cast doubt on claims UK and EU officials are talking about delaying Brexit if MPs reject Theresa May's withdrawal agreement.
- German and Irish foreign ministers meet to try to find a "fix" for the Irish border backstop
- A new government website advising consumers and businesses what to do in a no deal situation goes live on Tuesday, backed by a radio advertising campaign
- MPs write to the head of the Met Police saying they have "serious concerns" about public order and security outside Parliament, after Tory MP Anna Soubry was verbally abused outside Parliament by pro-Brexit supporters
Mrs May appears to be facing a growing backlash against a possible no-deal Brexit - if her agreement is voted down next week.
It is understood during Tuesday's Cabinet that Ms Rudd, a former home secretary who was a leading figure in the 2016 Remain campaign, told MPs history would take a dim view of the government if it accepted no deal and it would leave the UK a less safe country.
"We have to face the world as we find it, not as we wish it to be, and we have to deal with the facts as we find them," she is reported to have said.
While she wanted Brexit to go ahead, she said it was important that Parliament tried to reach as much of a consensus as possible.
"More than ever we need to find the centre, reach across the House and find a majority for what will be agreed. Anything will need legislation."
Home Secretary Sajid Javid said no deal would limit the government's ability to return illegal immigrants to other EU countries.
And Environment Secretary Michael Gove said that those considering rejecting Mrs May's agreement in the hope of securing a better deal "were like swingers in their mid-50s waiting for film star Scarlett Johansson to turn up on a date".
Ms Rudd added "or Pierce Brosnan", only for Justice Secretary David Gauke to quip that it was like "waiting for Scarlett Johansson on a unicorn".
Leading Brexiteer Steve Baker, the ex-minister who was a key figure in the failed attempt to remove Theresa May as Conservative leader last month, tweeted that the swingers' allusion was "not persuasive nor impressive".
On Monday, Business Minister Richard Harrington became the first minister to publicly say he would resign if the government pursued a no-deal exit and told the BBC others could follow suit.
His boss, Business Secretary Greg Clark, told MPs on Tuesday a no-deal exit "should not be contemplated" because of the likely impact on business..
MPs seek to curb no-deal powers
Meanwhile, a cross-party group of MPs, headed by Labour's Yvette Cooper and Conservative Nicky Morgan, will later attempt to make it harder for the UK to leave the EU without a deal.
The MPs have tabled an amendment to the Finance Bill in the hope of stopping the government raising money to implement a no-deal Brexit, without the explicit consent of Parliament.
The technical changes to a crucial piece of government legislation are intended to demonstrate to the government the strength of opposition to a no-deal Brexit in the Commons.
Government sources warned over the weekend of "paralysis" and an effective "shutdown" if the Treasury was stripped of the power to pass regulations relating to "no-deal financial provisions" without parliamentary approval.
Labour have said they will back the amendment, prompting speculation that ministers will be forced to accept it in order to avoid a damaging defeat.
If the government does not back down, a vote on the amendment is expected at about 19:00 GMT.
Brexit delay reports played down
The UK is scheduled to leave the EU on 29 March whether there is a deal or not.
The deal which Prime Minister Theresa May has negotiated with the EU - which covers the terms of the UK's divorce and the framework of future relations with the EU - has not been formally approved.
MPs are expected to vote on 15 January following five days of debate in the Commons.
Brexit Secretary Stephen Barclay has said the UK remains committed to leaving on 29 March after the Daily Telegraph said UK officials had been "putting out feelers" about extending Article 50, the mechanism taking the UK out of the EU.
Mr Barclay said he had not spoken to the EU about that and any delay would cause "some very practical issues".
His remarks came the day after Digital Minister Margot James suggesting Article 50 might have to be extended in order to stop a no-deal Brexit if Mrs May's deal is rejected by Parliament.
The BBC's Brussels reporter Adam Fleming said extending Article 50 was the "default" back-up plan for the EU if MPs did not agree to the Brexit deal, although he was not aware of any officials who had discussed it at this stage.
A no-deal Brexit would see the UK leave without a withdrawal agreement and start trading with the EU on the basis of World Trade Organization rules, an outcome favoured by some Brexiteers.
David Davis, one of Mr Barclay's predecessors as Brexit secretary, told the BBC the fact that EU officials were talking about re-opening negotiations "tells you that Mr Barclay's assertion that this is the only deal on the table is not, actually, entirely accurate".
"Because what actually is going on, is the Europeans are thinking about the next stage, and the next stage is another round of negotiation," he told Radio 4's Today.
He was speaking after Irish premier Leo Varadkar said the EU would offer the UK government fresh "written" assurances to help Mrs May get her deal through Parliament.