Tory ministers have rallied round Theresa May after her conference speech on Wednesday was marred by mishaps.
First Secretary of State Damian Green said it was "nonsense" to suggest she should quit because her speech was interrupted by a cough and a prankster.
He said the prime minister was "as determined as ever" to get on with the job. Home Secretary Amber Rudd said Mrs May was doing an "excellent job".
But ex-minister Ed Vaizey said "quite a few people" wanted her to quit.
The BBC's Laura Kuenssberg said that while many MPs wanted her to stay as leader, there were "emerging plots".
These involved Tory MPs trying to gather support to approach Mrs May privately and persuade her to stand aside.
This group will only act if they feel they have the numbers to do so "quickly and cleanly", the BBC political editor added, saying: "It is just not clear at the moment where the numbers really lie."
Speaking on BBC Radio Oxford, Mr Vaizey, who was sacked as a culture minister when Mrs May became leader in 2016, said most people were being "pretty loyal" in public but were "very concerned" in private. He added: "I think there will be quite a few people who will now be pretty firmly of the view that she should resign."
What now for May?
By Laura Kuenssberg, BBC political editor
Politics is certainly cruel, and clearly the prime minister was the victim of some appallingly bad luck.
A former minister told me that after the election and Grenfell it would only have taken one more event to trigger her exit and this "was the event".
In normal political times, it is probably the case that what one minister described as a "tragedy" would have led to a prime minister being forced out or quitting.
But these aren't normal times. Allies of Theresa May say Wednesday's events have shown her resilience and determination in spades, demonstrating exactly why she deserves to stay in the job.
But speaking on BBC One's Question Time Mr Green said: "I know that she is as determined as ever to get on with her job - she sees it as her duty to do so. She will carry on and she will make a success of this government".
He said it was "complete nonsense" to suggest that having a cold or having an "unfunny pillock" interrupt her speech meant she was the wrong person for the job.
The PM's speech was seen as her opportunity to assert her authority, after her decision to call a snap election backfired.
She apologised to activists and put forward new policies, including an extra £2bn to build 25,000 new council houses and social homes for rent by 2021 and draft legislation for a cap on standard tariff energy bills, which she said were part of her mission to improve people's lives and promote a "British dream".
But a nagging cough and croaky voice forced the PM to stop on more than one occasion. Prankster Simon Brodkin - also known as his TV persona Lee Nelson - was arrested by Greater Manchester Police after briefly interrupting the PM and giving her and a mock P45 redundancy notice he claimed was from Boris Johnson.
To add to Mrs May's woes, some of the letters fell off the conference stage backdrop behind her. By the end it read: "Building a country that works or everyon."
Cabinet ministers including Mr Johnson, Michael Gove and Jeremy Hunt have praised the speech and a No 10 source said colleagues had been "offering support" and declared "resignation is not an issue" for Mrs May.
But backbench Tory MP Mark Pritchard said on Twitter that a "small number" of colleagues were raising questions over her leadership in text messages.
Mr Pritchard, one of Mrs May's trade envoys, warned those "circling above" that there was only one message: "There is no vacancy at No 10."
And his colleague Charles Walker, vice chairman of the 1922 committee of backbench Tory MPs, praised Mrs May's "heroic" efforts on stage, telling the BBC: "You are actually allowed to be ill occasionally and that's what she was, ill - and she was ill because she's been working so damn hard on behalf of this country."
Ex-chancellor Lord Lamont warned against "political instability" during the "massively important" Brexit negotiations.
"I think what people ought to remember before they pitch in is that we are facing a very serious situation at the moment," he said.
Speaking on BBC Radio 4's Today programme, Business Secretary Greg Clark said people admired the "poise" and "guts" the PM showed to get through her speech.
He also said the fact that a comedian was able to get within yards of the prime minister showed a "weakness in the system".
Security at future Conservative events is to be reviewed. The prankster, Mr Brodkin, was later released by police who said he had "legitimate accreditation" to attend the event.
Former Conservative deputy chairman Lord Ashcroft said there was an air of a party that did not "know what it is doing".
But Business Minister Margot James told the BBC's Daily Politics she believed the coverage of the speech had been "pretty vicious" and Theresa May was "a very good prime minister".
Asked about reports of MPs plotting against her, Ms James said: "I think there will be a small minority of disaffected colleagues who are angry, bitter for whatever personal reasons they've got, and I do hope my other colleagues will have the sense to disown them."