Environment Secretary Michael Gove has urged his colleagues not to back a Commons vote on delaying Brexit.
Mr Gove said it would be the “wrong thing to do” if cabinet ministers Greg Clark, Amber Rudd and David Gauke supported the bid, which would push back the UK’s exit date of 29 March.
Speaking to the BBC’s Andrew Marr, Mr Gove refused to say whether they could keep their jobs if they backed a delay.
Theresa May told Tory activists on Saturday Brexit must not be frustrated.
She said to the group that as her negotiations with the EU reach their final stages, the “worst thing we could do is lose our focus”.
The trio made their intervention in the Daily Mail, saying they would support moves to extend Article 50 – the legal mechanism to see the UK leave the EU on 29 March – to avoid a “disastrous” no deal Brexit, unless a deal is agreed “in the next few days”.
But Mr Gove said: “It’s not just about a potential extension of Article 50, it’s about taking power away from the government. And who knows where we might end up?
“We might end up with a second referendum, which would do real damage to our politics.”
Mr Gove said progress was being made in Brexit negotiations between the UK and EU but that he did not know if there would be a final vote on the Brexit deal in the Commons this week.
On Wednesday, MPs will be able to put forward a range of amendments to show what direction they want Brexit to take.
One, tabled by Labour’s Yvette Cooper and Conservative Sir Oliver Letwin, would give Parliament the opportunity to delay Brexit and prevent a no-deal situation if there is no agreement with the EU by the middle of March.
In the Daily Mail. Business Secretary Mr Clark, Work and Pensions Secretary Ms Rudd and Justice Secretary Mr Gauke said if the European Research Group of pro-Leave backbench Tory MPs stood in a way of the withdrawal deal, they would be forced to vote for the amendment.
The ERG would then have “no one to blame but themselves for delaying Brexit,” the trio said.
Tory MP and leader of the ERG, Jacob Rees-Mogg told BBC Radio 5 Live’s Pienaar’s Politics that, for ministers, “the act of voting against the government is the act of resignation”.
The prime minister has said there must be no party “purges” over MPs with differing views.