A survey of more than 500, carried out by shropshirestar.com, called for the deal to be ratified by Parliament during an unusual Saturday sitting.
It comes as shoppers in the county spoke of their disillusionment of the whole process.
Margaret Wild, 83, from Kenley, near Shrewsbury, said: “I think we voted for out and we must come out.”
Mrs Wild said as a farmer’s widow she had some reservations about the deal Boris Johnson had struck with the EU, but said MPs should respect the will of the people.
“I think he’s made the best of a bad deal, and I just hope the rest will see the light and we go through with it,” she added.
Alwyn Williams, 71, of Llanfyllin, voted to remain and said he would like to see Mr Johnson’s deal put to a second referendum.
He said: “I was quite surprised that he got a deal, but as one who voted to remain I’m quite surprised that is still on the anvil.
“I would like to see a return to the people and a people’s vote, I know people say we will want a second, a third and a fourth, but I think if we have another it could be quite decisive if it goes one way or the other. I suppose the danger is if there is a split again.
“It’s taken three years, and no decision has been made at all. It’s in the balance.”
Keith Seanor, a Remain supporter from just outside Shrewsbury said he believed Mr Johnson’s deal would lead to the break-up of the United Kingdom.
“If that deal gets passed, Ireland will unite, Scotland will get independence, and Wales will go for independence,” he said.
Mr Seanor said his wish was for Article 50 to be revoked, and had no desire to see another referendum, adding: “I think it’s far too complicated for the average person. I think people voted to leave because they have been subjected to propaganda.”
Daphne Beddow, who lives in Codsall, said the in-fighting in Parliament needed to be finished – along with Brexit. The 69-year-old said: “I think they should get on with it – and they squabble like children.”