Lord Patten, the former chairman of the Conservative Party, has warned Tory MPs the party will lose the next election if it appears to be divided or obsessed with plotting against David Cameron.
Speaking to journalists in Westminster on Thursday afternoon, Lord Patten, who now serves as chairman of the BBC Trust, said it was "very difficult to lead any party which isn't united and win an election"
"I think parties which aren't totally united don't win elections. And what used to be one of the most important characteristics of the Conservative party, and I hope still is, it was more interested in running the country than who ran the Conservative Party," he said. "That's why the Conservative Party had been around longer than any other."
"I think if you lose sense of being united, if people start to think you're more interested in fighting one another than fighting for the country, then the game is up," he said.
His warning came on the same day business minister Michael Fallon all but confirmed home secretary Theresa May was manoeuvring to take over the leadership from Cameron.
On Thursday morning bookmakers Ladbrooks installed May as favourite to be next Tory leader, cutting the odds from 6/1 to 4/1.
Lord Patten, who was chairman of the Conservative Party at the time of John Major's 1992 general election victory, also recognised Cameron had trouble managing the eurosceptic demands of his backbenchers.
"The Conservative Party has since the mid-1990s had difficulties with the European issue. Though not I think in 1992 when we fought the election pretty straight on a pro-Maastricht manifesto and won more votes than the Conservative Party won for some time. More votes than Tony Blair won in 1997.
"Since then the Conservative Party has had arguments internally about Europe. And Conservative leaders have had a problem straddling their view of the national interest and the management of the Conservative Party.
Asked about the prime minister's strategy to renegotiate Britain's membership with the EU in order to bring some powers back to London, Lord Patten said that should be "perfectly possible" without the UK "being drawn into European enterprises which hold unacceptable sacrifices in political sovereignty".
And he said Tory MPs who believed no renegotiation would be acceptable was suicidal. "If your response to that is nothing will be acceptable, then I think that would be bad news for the Conservative Party," he said.
Quoting Winston Churchill he added: "It is never necessary to commit suicide, especially when you may live to regret it."
Cameron has to deal with backbenchers who are more rebellious than any of any party since 1945 - with a substantial number of rebellions having come on the issue of Europe.