Refusing to debate live on TV with Nigel Farage during the general election campaign would be "catastrophic" for the Tories' chances of victory, leading party activists have warned David Cameron.
The Conservative Grassroots group has sent the Prime Minister the results of a poll showing a majority of voters believe the Ukip leader should be allowed to join any repeat of the 2010 televised showdowns.
Mr Farage has stepped up his claim for an equal billing after emerging the clear winner amongst viewers of two clashes with Deputy Prime Minister Nick Clegg ahead of the May 22 European elections.
At the last election, the Liberal Democrat leader enjoyed a significant boost in public support after taking part in the debates alongside Mr Cameron and the then Labour prime minister Gordon Brown.
But the Tory leader has made it clear he does not believe the eurosceptic party should be represented, insisting the showdowns "predominantly should be about people who have a prospect of becoming Prime Minister".
Labour leader Ed Miliband has also expressed his opposition - amid fears the Tories will use the Ukip dispute to scupper ongoing negotiations about an acceptable format.
There appears, however, to be a public appetite to see Mr Farage take on his major rivals - leading to demands for Mr Cameron "take the fight" to Ukip.
A survey by ComRes, commissioned by Conservative Grassroots, found voters backed his inclusion by 51% to 21%.
And by an even wider margin (53% to 20%) they said Mr Cameron would look like a "coward" if he did not take up the challenge - among them almost half (49%) of Conservative supporters.
The group's chairman Robert Woollard said attempts by Mr Cameron to combat the threat of Ukip by being "rude" about its members had "backfired".
With the party in danger of being pushed into third place in next month's European elections, and Ukip tipped by some to top the national poll, the high-risk strategy of a head-to-head contest was the only remaining option, the party members said.
"What this poll clearly demonstrates is that the public want and expect Nigel Farage to be included in the televised debates championed by Fleet Street and broadcasters like Sky," ex-local party chairman Mr Woollard said.
"It shows that if the political establishment tries to deliberately close out the Ukip leader it will be completely counter-productive and drive voters into his camp.
"And we know that this could have a catastrophic effect on our chances of winning the next general election and keeping out the discredited Labour Party."
Mr Cameron and other senior Tories " have tried to reverse the inexorable rise of Ukip, by being rude about their members, dismissive of their impact, even highly personal about Mr Farage - all of which have backfired", he said.
"The PM must know that the very definition of insanity is always doing the same thing and expecting different results. So it is time to take the fight to Nigel Farage and win the policy argument.
"We believe that only by winning the argument against Ukip does Mr Cameron stand any chance of holding on to No 10."
Watchdog Ofcom ruled recently that Ukip should be treated as a major party in England and Wales by broadcasters covering this year's European elections.
The decision means Ukip will be given the same status as the Conservatives, Labour and Liberal Democrats for election broadcasts and news coverage of the May 22 contest.