But members of the European Research Group (ERG) said they would not back today's motion unless the wording was changed, risking embarrassment for the government and undermining attempts to secure concessions from Brussels on the Brexit deal.
Shadow Brexit secretary Keir Starmer said Mr Barclay was "all over the place on all of the important issues", and accused Mrs May of "running down the clock, hoping to get to March or even the end of March" before presenting MPs with a choice of her withdrawal agreement or a no-deal Brexit.
"The Prime Minister has done a pretty good job of standing up to them up till now, but they were drinking champagne to celebrate her losing her deal and I regard that as being treachery", he said.
Mark Francois, vice-chairman of the ERG, said: 'We can not vote for this as it is now configured because it rules out No Deal and removes our negotiating leverage in Brussels'.
May is expected to be able to weather a defeat on the Government motion, but it would be another embarrassing blow as she seeks to get the European Union to agree to changes to her deal.
Veteran Tory Europhile Kenneth Clarke has tabled a further amendment, backed by senior figures from across the House, including Labour's Harriet Harman, which would allow MPs to vote for their preferred Brexit outcome.
MPs will again vote on options for Brexit today, with Eurosceptic Conservatives threatening to oppose a motion put forward by Theresa May.
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Ms Leadsom defended Mrs May's decision not to remain in the Commons to hear the result of Thursday's vote: 'The Prime Minister just this week spent two hours and 18 minutes answering questions in the chamber.
"If she carries on like this, then we all know what is going to happen".
She has promised that if parliament has not approved a deal by February 26, she will make a statement updating lawmakers on her progress on that day and lawmakers will have an opportunity on February 27 to debate and vote on the way forward.
The Liberal Democrats' Tom Brake asked: "In what way can we as members of Parliament, who have already voted to rule out no deal, can ensure that the government listen to that and respond appropriately?"
"I'm afraid people didn't want to be treated like that twice".
In an interview with Parliament's The House magazine, conducted before the vote, he said they had celebrated after Mrs May was defeated in last month's vote and were not true Conservatives.
This third amendment, led by the Conservative Anna Soubry and Labour's Chuka Umunna, could prove particularly problematic for Mrs May, who has lost previous votes calling for government documents to be published.