Some Leave-backing MPs may not want to cause instability which could risk Brexit not happening, while others may feel a leader who backed their side in the referendum is better placed to lead the United Kingdom in talks.
She began by apologising for sparking the costly June election which cost her party its majority in parliament, almost handing over power to Labor under Jeremy Corbyn.
'Now what the country needs is calm leadership, and that's what I am providing with the full support of my Cabinet, ' she said.
It comes following the critical response to her speech at the Conservative Party Conference last weekend - as well as ongoing disagreements over Brexit.
The prime minister's speech, which was meant to rally the Tories after weeks of in-fighting, was interrupted by comedian Lee Nelson (real name Simon Brodkin) who handed May a fake P45.
Her aides sought to spin the speech as showing May's human side, countering the image of her being a "Maybot" who uttered scripted lines and answers during her election campaign.
"She was happy, pleased with the way it worked", said a source.
In recent weeks, foreign secretary Boris Johnson has made it clear that he would like to be fired from his post in the cabinet so he can focus on causing trouble, whining about Brexit, and pushing his own leadership bid.
The i newspaper writes that coughing fits, a man handing her a P45 and a collapsing stage-set ruined May's key address.
As speculation mounts over the Prime Minister's future, here is a look at how Theresa May could be replaced. The content of the Prime Minister's speech in Manchester this week demonstrated clearly that she has a plan to make our country better for everyone.
But she is under growing pressure over negotiations in Brussels, while the increasing popularity of Labour leader Jeremy Corbyn poses a threat.
Gove said on the show: "No one is burying their heads in the sand".
Damian Green said it was "nonsense" to suggest she should go over the speech.
Shapps defended his decision to challenge May's leadership, saying: "We're not on the right path and the answer - after a frankly disastrous election - to have a new leader is hardly a radical thought".
MPs elected in June are reluctant to move against the prime minister, given they've only been in office less than four months.