Former prime minister David Cameron said Mrs May would have to change her approach to Brexit as a result of the election.
"They would see it as the government paying cash for votes in parliament". He argues that without that option, the government's position would be weakened.
Foreign Secretary Boris Johnson, who is also touted to replace Mrs May should she be forced out, wrote in The Sun newspaper that people "have had a bellyful of promises and politicking", and that "now is the time for delivery - and Theresa May is the right person to continue that vital work".
The resignations were reportedly demanded by Tory MPs as the price of their supporting the Prime Minister.
May is also said to have expressed her apologies to the MPs who had lost their seats in the snap election which she had called.
Gove said he rejected the terms "soft" and "hard" Brexit because "I'm never sure what they mean" and that the term "hard Brexit" was invented by people who want Brexit to be seen as "some sort of punishment". Labour surpassed expectations by winning 262.
Many senior Conservatives say May should stay, for now, to provide stability.
"It is our job to get on with running the country".
Theresa May has apologised to Tory MPs for the party's election performance, telling them "I got us into this mess I'll get us out of it".
He acknowledged that the government would now be unable to get numerous measures promised in its election platform through Parliament.
She has promised to start the formal Brexit talks next week but her authority has collapsed since the election result and opponents took her woes as a chance to push back against her Brexit strategy.
May addressed a packed meeting of the 1922 Committee for 90 minutes after her failure to win the election outright prompted days of speculation about her future. But even if that game goes into extra time, European Union leaders are making clear to May that there can be no extension to the two-year period of negotiation before Britain must leave Europe in March 2019. "The union as I've said before is our guiding star", she said.
May is due to hold a meeting at Downing Street Tuesday with DUP leader Arlene Foster to discuss the working relationship between the two parties.
"The DUP may never have the political arithmetic so favorable again so like the Conservatives, the DUP will want to avoid another election and will want to keep drinking in the political free bar that is available to it", Tonge said.
The Tories and the DUP are considering a "confidence and supply" arrangement which would see the Northern Irish party back the Government to get its Budget through and on confidence motions.
The alliance makes some modernizing Conservatives uneasy. While the DUP is popular in Northern Ireland, many in the rest of the United Kingdom will find the party's values unpalatable.
It comes as the party has accused the DUP of betraying the interests of Northern Ireland by agreeing to prop up a Conservative minority government.
Former Conservative prime minister John Major has also raised doubts about the deal and its impact on the province's "fragile" peace.
The British government doesn't have long to ink a deal.
Both sides expect a deal to be agreed on Wednesday, which would guarantee the DUP's support for Ms May's minority government on important votes.
But First Secretary of State Damian Green said he could not confirm the Queen's Speech will proceed as planned on 19 June. Without the amendments, he said Labour would try to vote down the speech.
"I think there will be pressure for a softer Brexit", Mr Cameron added, saying that Parliament now "deserves a say" on the issue.
Meanwhile, German Finance Minister Wolfgang Schaeuble said it's not too late for the U.K.to change its mind.