The Prime Minister prompted fury among many Conservatives by reaching out to Labour leader Jeremy Corbyn in the hope of finding a consensus solution to Brexit ahead of a crunch EU summit on April 10.
And Mike Stathers, chairman of the East Riding Conservative Association and a representative on East Riding of Yorkshire Council, said he was "appalled" at the change of approach.
He told The Yorkshire Post: "Members have kept very good contact with our MP Sir Greg Knight in recent weeks, he has informed us of his weekly activity in terms of how he has been voting.
"But I have to say I told Sir Greg last night that I was appalled at the Prime Minister's decision to involve Jeremy Corbyn at this very late stage. I have spoken to several other members of the association who have a similar view. We have made our views known to Sir Greg.
"I am seeking re-election. I have been on door-knocks for the last two weeks or so and the first thing on people's minds is Brexit, and 'what are you going to do?'. As district councillors we can't do a great deal about Brexit.
"I have to say there is some real concern about the impact that Theresa May's decision-making might have on traditional Tory voters on May 2. The worry is that they won't turn out. We are saying 'please turn out, it is local issues that matter."
Dale Smith, chairman of the Shipley Conservative Association in West Yorkshire, said: "What I am saying to anyone who asks is 'keep calm, let's see what happens and make a judgement in due course'.
"The whole process was going to be fraught with difficulties from the word go. It is not surprising to me personally that we have arrived at this impasse. Everyone is at 6s and 7s.
"All we can do is keep calm, wait to see what happens and make a judgement on it. The Prime Minister has got to be given head room to try and deliver the deal that she is urging upon us all.
"The members are divided. People keep talking about the 17 million majority, but they forget the 16 million who voted for the contrary, of which I was one."