Former minister Nick Boles, who voted Remain, said the plan was a "desperate last move" and the prime minister was losing the confidence of colleagues from all sides.
The backlash came as Ms May and European leaders gave press conferences, after a key EU summit broke up without a Brexit deal.
If you want to follow the events as they happened, see our live coverage below
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Breaking: Theresa May has told journalists she is considering asking for a longer transition period in a bid to break the deadlock in the Brexit talks.
My colleague Jon Stone is at the European Council summit in Brussels and has filed this report, where the PM confirmed the big overnight story about an extension to the transition up to the end of 2021.
Tory former minister Nick Boles said any attempt to extend the transition period was a "desperate last move" and warned Theresa May she was losing the confidence of her colleagues.
"It's a classic of negotiations that she keeps on thinking that one more concession is going to somehow, with one bound and she's free and she's not going to be free, she's getting ever more trapped," he told the Today programme.
"I'm afraid she is losing the confidence now of colleagues of all shades of opinion, people who have been supportive of her throughout this process.
"They are close to despair at the state of this negotiation because there is a fear that both the government and the European Union are trying to run out the clock, that they are trying to leave this so late that they can credibly say there is no alternative but a no-deal Brexit and most people agree that would be chaos.
"That is not an acceptable way for a leader of a government to behave."
Great pictures from last night at the European Council summit, where German chancellor Angela Merkel, French president Emmanuel Macron, Belgian prime minister Charles Michel and Luxembourg prime minister Xavier Bettel were spotted having a drink.
Angry senior Tories have accused Theresa May of going back on her pledge to allow a proper “meaningful vote” on any Brexit deal and vowed to fight the move.
Ken Clarke and Dominic Grieve spoke out after the government said MPs should only be allowed to accept or reject the agreement – with no amendments allowed.
David Lidington, the de-facto deputy PM, said how much it would cost to extend the transition period was something that would have to be "teased out" during the negotiations.
Asked if it would only be for a few months, he told Today: "Yes, that is certainly the intention. That is how we see it. That is something that is now in the mix with the negotiators."
Mr Lidington dismissed claims by some former Cabinet ministers that the details of the Irish backstop had not been clear when it was signed off in principle last year.
He said: "Cabinet ministers are sensible and responsible, intelligent people who look at the documents before they endorse them."
Richard Tice, who co-chairs the Leave Means Leave campaign group, said the transition was "an unnecessary trap created by our weak civil servants" who are trying to thwart Brexit.
He said: "It should be cancelled, not extended. It is increasingly clear the PM doesn't want to leave either.
"Any transition period gives the EU zero incentive to negotiate anything and gives Brussels the power to force whatever they want on to the UK without us being able to do anything about it. It's downright dangerous."
European Parliament president Antonio Tajani has said he may visit Ireland to outline their support in protecting the Irish border.
He met with Taoiseach Leo Varadkar on Thursday morning, when he confirmed parliament's commitment to the backstop which he described as a "key element".
"Without it we cannot vote in favour of the agreement," he said in a press conference.
"I may visit Ireland to explain Parliament's position which is in full support of the Republic of Ireland."
He told Mr Varadkar that he repeated their position on the border which he said needs to be flexible to protect peace and the Good Friday Agreement.
Voters will not forgive Theresa May if she surrenders to Brussels in the Brexit negotiations, Boris Johnson and David Davis have warned.
In an open letter to the PM, published in the Telegraph, they claimed her plans for future relations with Brussels were less popular than the poll tax and called on her to "deliver the Brexit which people voted for".
It was signed by former cabinet ministers Mr Davis, Mr Johnson, Iain Duncan Smith, Owen Paterson and Priti Patel, as well as Jacob Rees-Mogg, chairman of the Conservative European Research Group of Brexiteer Tories.
It said: "We urge you to make clear that you will not bind the UK into the purgatory of perpetual membership of the EU's customs union, whether by a backstop or any other route."
It adds: "Talk of either a UK or a Northern Irish backstop is inimical to our status as a sovereign nation state. Both are unnecessary: indeed they are a trap being set by the EU which it is vital we do not fall into."
The group called on Mrs May to "reset" the negotiations and ditch her Chequers Brexit blueprint.
"We urge you not to engage in a show of resistance and a choreographed argument followed by surrender and collapse into some version of the backstop and Chequers," they wrote.
"Instead we urge you to say to the EU at the summit: 'Let us agree that we need to reset our negotiations. Our objective is a free trade agreement that benefits the UK and EU and millions of our citizens.'
"This would command a majority in Parliament, unlike the unpopular Chequers plan. Let us seize the opportunity and create a better future for the UK."
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