Officers of the Tory backbench 1922 Committee were meeting in Westminster yesterday evening to consider proposals to change party rules to allow MPs to challenge Mrs May's position as leader as early as June.
Tadhgh Enright joins us in the studio.
"I really believe at the moment ... where parliament has to decide what it wants to do in weeks, a leadership election would be disastrous, not just for the Conservative party, but for the whole country", he told the BBC.
Pro-Brexit Conservatives are angry with May's failure to take Britain out of the European Union, nearly three years after voters backed leaving.
Officials from the party's committee of MPs met on Tuesday to discuss the plans but the meeting was said to have been inconclusive.
The Brexit Party leader said he meant to echo the words of the Labour peer, which were "helpful", adding: "Please five million Labour leavers, I want your vote".
TIG MP Angela Smith tweeted: "Such a shame to see a great anti-Brexit campaigner reduced to repeating meaningless lines from the Labour leadership".
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May's official spokesman told a regular media briefing that the government's position was that progress needed to be made urgently as it was vital to deliver on the result of the 2016 referendum when people voted to leave the European Union by a 52-48 margin.
Corbyn said the government had so far refused to move on the terms of May's Brexit deal which MPs have already rejected three times, once by the biggest margin in British political history.
Lord Adonis is standing in the May 23 European Parliament elections for Labour in the South-West of England, where he faces opposition from Rachel Johnson fighting for TIG under the banner Change UK and former minister Ann Widdecombe for the Brexit Party.
"I think she's lost the trust of grassroots members and that's the worrying thing".
She said: "I'm afraid the prime minister is conducting negotiations in such a way that the party does not approve".
Mrs May has come under heavy criticism for her handling of the Brexit process, but survived a vote of confidence by her MPs in December.