George Osborne says May is a "dead woman walking" and Anna Soubry says May's position is "untenable".
The 60-year-old is struggling to reassert her authority after losing her parliamentary majority in Thursday's snap election, just days before Brexit talks begin. He said a new election might be necessary later this year or early in 2018.
It follows the resignations of her co-chiefs of staff Nick Timothy and Fiona Hill whose abrasive style upset ministers and who were blamed by many in the party for the abysmal election campaign.
Conservative lawmaker Nicky Morgan told ITV that she could support a confidence and supply arrangement with the DUP, but any closer deal would be "a step too far".
The talks were in line with DUP leader Arlene Foster's "commitment to explore how we might bring stability to the nation at this time of great challenge", her party said in a statement.
The prospect of being propped up by the socially conservative DUP, which is strongly focused on Northern Ireland's specific political complexities, was causing concerns in the Conservative party, senior lawmaker Graham Brady said.
The DUP is strongly opposed to single-sex marriage and abortion, at odds with Conservative policies.
On Brexit, Mr Corbyn said he wants a "jobs-first Brexit" negotiated as quickly as possible along with guaranteeing the post-Brexit rights of European Union nationals living in the UK.
If neither party can command a majority in parliament for their Queen's Speech, it is likely a fresh election would be called.
"I asked for a categoric assurance that if any deal or scoping deal was done with the DUP there would be absolutely no rescission of LGBTI rights in the rest of the United Kingdom, in Great Britain, and that we would use any influence that we had to advance LGBTI rights in Northern Ireland", said the MP, who is a lesbian.
Uber set for changes after board reviews report on workplace culture
Holder Jr.in his report on the probe into the Uber's work culture is also going to be a big talking point at the meeting. Michael is a close friend and ally of Kalanick , which would make his presence during the investigation rather tricky.
"It's very hard to see how a hard or disruptive Brexit can come out of this", Tony Travers, professor of politics at London School of Economics, said in an interview.
Fallon said the change in circumstances would require "a more collective approach" in government, but he also said he expected Conservative lawmakers to "rally behind" May when they meet early next week.
May's office said Saturday principles of an agreement had been reached, but the two sides later clarified that they are still talking.
Primer Minister Theresa May leaves Downing Street on her way to Buckingham Palace in London after Britain's election.
It feels like a lifetime ago that May called the election, saying she needed a large majority so that she could get the best Brexit deal.
"I don't think she does have a majority in the House of Commons for leaving the single market", Anna Soubry, who campaigned for Britain to stay in the European Union ahead of last year's referendum, told Sky News.
"I don't think Theresa May and this government have any credibility", Corbyn told the Sunday Mirror, predicting that there could be another election within months.
In a measure of the desperation in Conservative ranks, Brady, who is chairman of the influential 1922 committee of Conservative lawmakers, suggested the party could end up relying on support from pro-Brexit opposition members of parliament.
Seven Republican Sinn Fein members who want a united Ireland were also elected on Thursday, but they do not attend or vote as the party does not recognize Westminster rule. She's now attempting to form a government.
He tweeted that an article in the Mail on Sunday newspaper headlined "Boris set to launch bid to be PM as May clings on" was "tripe".
"There's a possibility of voting the Queen's Speech down and we're going to push that all the way". May has said her government will go ahead with these discussions as planned.