"It is a grave mistake for any prime minister to fail to recognise when a plan will not work and it is fatal to press on regardless," Williamson wrote in a newspaper op-ed.
But her ministers came out fighting today, saying the Government was focused on securing a "stable majority" to get its Brexit bill through Parliament, and that meant dealing with the opposition.
"What's the alternative?" Education Minister Damian Hinds said on the BBC's Andrew Marr Show. Both sides were negotiating in "good spirit" and he was still hopeful of progress, he said, adding that if talks fail, the next step will be votes on Plan B options in Parliament. "We have to find a way through and that means we have to have a majority."
Justice Minister Robert Buckland told Sky News the Government was determined to get its Brexit bill through Parliament, and the threat posed by Farage's party should push MPs to get behind the deal.
"Parliament's in the dock" over Brexit, he said.
In recent weeks, there have been periodic signs that a deal is possible. Labour wants one that protects workers' rights and the environment, and for a customs union with the EU, and May has indicated the two sides aren't far apart. Shadow Trade Secretary Barry Gardiner told Sky News the biggest issue remains what happens after May leaves office.
"Even if we can come to a deal, we don't know if the successor to Theresa May will deliver on it, and that's one of the biggest sticking points," Gardiner said.
The party is just as divided on Brexit as the Conservatives, though, and Gardiner was forced to defend Labour's pursuit of a deal with the Government in the face of opposition from its members - the majority of whom want it to campaign to stay in the EU.
Labour is trying to "bail out the country" and has consistently pledged to honour the result of the 2016 referendum, he said.
That stance was rejected by former Prime Minister Tony Blair, who argued that it was a "fallacy" to expect that a soft Brexit deal - one keeping close ties to the EU after leaving - could unite the country. The only solution was for Parliament to reach a decision that is then put to another referendum, he said.
"That soft Brexit is never going to command anything other than a tiny amount of support," Blair told Sky's Sophy Ridge on Sunday show. "The people who want Brexit will say it's a betrayal and the people who want to remain will say it's completely pointless."
With both major parties in turmoil, Farage is taking advantage. Corbyn faces losing Leave voters in Labour-held constituencies, while a survey by the Conservative Home website, published in the Times newspaper, suggested three in five Tory members are planning to back Farage's Brexit Party on May 23.
Buoyed by those polls, Farage put in a typically combative interview on the Andrew Marr Show, repeatedly denying that his position had changed on leaving the EU without a deal since the 2016 referendum. He said the Brexit Party was unequivocally for a "clean" split from the bloc - a move he said would put pressure on the EU to sign a free-trade deal.
He accepted that a so-called hard Brexit would cause "short-term economic disruption," but likened it to moving house. "This is our future," he said.
- Bloomberg
