Baker said 80 or more lawmakers were prepared to vote against the plan. That's been one of the thorniest issues in the Brexit negotiations.
Sarah Wollaston, chairwoman of the Commons Health Select Committee, said Mr Johnson was not "fit to lead the country" and indicated she would quit the party if he became prime minister.
Pro-Brexit Tories are said to have spent several hours plotting to oust her on Tuesday night because they think she's betraying their vision of a clean break from the EU.
He said however he personally was no part of any leadership challenge, while another MP who attended said only five or six MPs openly discussed removing May. The plan for a special Brexit deal summit is likely to be unveiled during the course of the Salzburg gathering, two people said, with one suggesting the announcement could come even sooner.
Barnier, the EU's chief negotiator, told a forum in Slovenia that it was "realistic" to expect a divorce deal with Britain, the British embassy to Slovenia said on Twitter.
The pound fell against the dollar to as low as $1.2994 on reports about lawmaker discussions about May's exit, but later recovered to trade flat at $1.3028. The UK will leave the European Union, with or without a deal, on 29 March next year. This is seen as critical by both sides, but talks have been deadlocked for months.
With just 200 days to go to the scheduled date of Brexit, Mr Baker said that the PM would lack credibility with Brussels negotiators if she tried to press ahead with her departure plan at the party conference without the backing of her party. Barring any further developments on trade, this Thursday's United States inflation and Friday's retail sales figures will be the key data points to look out for this week.
Barnier's comments also dragged the Euro upwards yesterday, given the degree to which a smoother Brexit would alleviate pressure on the Eurozone economy.
Mr Baker, a leading figure in the pro-Brexit Tory European Research Group, said the party's annual conference in Birmingham, starting on September 30, could prove a decisive moment as Mrs May is forced to acknowledge the scale of grassroots opposition to her proposals. This time, one subject dominated: how to get rid of May.
May's government says its critics have failed to present a viable alternative to her Chequers proposal.
Former Brexit Secretary David Davis, who quit the cabinet in July over the proposals, told reporters he expected May's government to change course on Brexit after an informal meeting of European Union leaders in Salzburg next week. On Wednesday, the ERG will put forward its own plan for resolving the Irish border question.
He told Newsnight: "If you listen carefully to what Michel Barnier said there was no movement, there was an expression of confidence that we can get an agreement on the withdrawal agreement where we are going to give them £39 billion".
London and Brussels say they want to get a divorce deal at the October 18 EU Council or at the latest by the end of the year.
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