Party colleagues rallied around the Prime Minister, but an ally revealed that backbenchers had voiced concern at her ability to continue following the mishap.
There were also calls for the chairman of the Conservative Party, Patrick McLoughlin, to resign over claims of a security breach after the prankster Simon Brodkin was accredited and allowed to get within inches of the Prime Minister.
Privately, there was astonishment among senior Conservatives over the display yesterday.
However, critics of Mrs May’s premiership are hampered by the lack of an obvious successor, and the desire to avoid compounding the chaos within their party.
The Prime Minister had gone into the conference in Manchester insisting she would lead her party into the next general election, but it is now highly unlikely that Mrs May will head another campaign.
MP Mark Pritchard said colleagues were texting each other about the Prime Minister’s calamity-ridden address but warned them “there is no vacancy at Number 10”.
Mr Pritchard revealed a “small number” of Tory MPs appeared to be on manoeuvres.
He tweeted: “For small number of MPs texting MPs asking what we thought of PM’s speech (or circling above) one message: there is no vacancy at Number 10!”
Mr Pritchard, who was last month appointed as one of Mrs May’s trade envoys, praised Mrs May for battling through the unexpected interruptions.
“Prime Minister to be praised for pressing on with speech, despite: coughing fit, stage set falling apart and a so-called comedian/prankster,”he posted.
Another MP, Matt Hancock, tweeted: “There are few things more inspiring than triumphing through difficulty. Our Prime Minister is doing just that right now with great humour”.
Boris Johnson, who has been widely criticised for his perceived disloyalty to Mrs May, which raised questions over whether he may challenge her leadership, praised the PM’s speech.
The Foreign Secretary tweeted: “Great job by the PM today putting housing at the heart of renewing the British dream”.
During the speech, cameras caught Mr Johnson being told to stand up for an ovation during the Prime Minister’s coughing fit by Home Secretary Amber Rudd.
Health Secretary Jeremy Hunt said he believed Mrs May’s speech showed a “great sense of duty”, adding she “did really well” to cope with a persistent cough and a prankster waving a P45 unemployment notice in her face.
Environment Secretary Michael Gove claimed it was “a fantastic speech from a Prime Minister at the top of her game”.
Philip Hammond, who came to the Prime Minister’s aid with a throat lozenge, told journalists: “Obviously nobody wants to be coughing in the middle of a speech, but she got over it and she showed her resilience.”
Scottish Conservative Paul Masterton, among MPs selected to speak on the main stage before Mrs May’s arrival, said: “It was a clear reminder why she’s the right person to be taking the country forward – a stinking cold, some idiot at the stage halfway through, and she did what leaders do.”