However, the National Conservative Convention, which represents 800 of the party's highest-ranking officers, will now call an extraordinary general meeting to discuss May's premiership.
The donors' comments come as two surveys revealed a Tory supporters were likely to turn their backs on the party and shift their support to Brexit Party during the European parliament elections.
It is just one of the calls that will be facing her from MPs, councillors and party workers after a hard two weeks of campaigning on the doorsteps of the country.
Responding to the challenge posed by Mr Farage and his Brexit Party, Mr Corbyn insisted Labour was not "worried about him", dismissing his platform as "simple populism".
'We won't beat him unless we can inspire the millions crying out for a different direction.
In desperation, at the start of the month she began talks with Labour leader Jeremy Corbyn to find a consensus, but initial discussions were unproductive and there are elements on both sides who oppose any such negotiations. It's that there are about five million people who voted Corbyn in 2017 and voted Brexit the year before, and I think that's where I need to be.
"We won't win if we sit on the fence about the most crucial issue that has faced our country for a generation".
In a tweet Mr Watson also said: "Labour won't defeat Nigel Farage by being mealy-mouthed and sounding as if we half agree with him".
Mr Corbyn insisted Labour was not anxious about Mr Farage, dismissing his platform as "simple populism".
Some 62% of the 1,132 Tory members surveyed by the ConservativeHome website said they would vote for Mr Farage's party in the European contest.
Writing in the Sunday Telegraph, International Trade Secretary Liam Fox said the EU will end up with 50 "disruptive and resentful" British MEPs if it forces the country to take part in European elections.
Elsewhere a new poll found former foreign secretary Boris Johnson is the favourite to replace Mrs May as Conservative leader among the party's grassroots.
The Labour Party has said that its priority is to achieve the best Brexit deal for jobs and living standards so they can improve the economy and invest in all communities.