Earlier, he was criticized for accusing May of wrapping "a suicide vest around" Britain and handing the detonator to the European Union with her plans for Brexit - the biggest shift in British foreign and trade policy for nearly half a century.
Mrs May's spokesman said Chequers was "the only serious, credible and negotiable plan".
The prime minister faces a torrid Conservative conference in Birmingham in early October, with Mr Johnson planning to address up to 1,000 party activists at a "Chuck Chequers" rally. The EU and Britain hope to clinch a deal later this year so parliaments on both sides can ratify it before Brexit.
Under the EU's version of the plan, if no trade deal with the United Kingdom resolved the issue, Northern Ireland would effectively remain part of the single market.
"I think it's possible" to get a deal by the start of November, Barnier said at a conference in Bled, Slovenia. We have wrapped a suicide vest around the British constitution - and handed the detonator to Michel Barnier.
The toxic atmosphere between the two wings of the Conservative Party was vividly illustrated in the reaction to Mr Johnson's incendiary Mail on Sunday column.
The likes of former foreign secretary Boris Johnson, Environment Secretary Michael Gove and Home Secretary Sajid Javid are expected to be among the runners and riders whenever the PM leaves Downing Street.
In Brexit negotiations, Mr Johnson said the country needed to learn lessons from Churchill, who showed "a willingness to be brave" during the Second World War.More news: Casey withdraws after 3rd round of BMW Championship
Mr Coveney said many would be offended by Mr Johnson's remarks and claimed it was an attempt to undermine British Prime Minister Theresa May.
"I'm sorry, but this is the political end of Boris Johnson".
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.
The former foreign secretary's extraordinary comments provoked an immediate backlash from Tory critics in the latest sign of the bitter Conservative divide over Brexit and the future leadership of the party.
'If you think back to the great achievements of the Thatcher era, it was about helping people to seize control of their own destiny, ' he told the American Enterprise Institute.
Sterling was trading strongly up on Friday last week after the European Union chief negotiator Michel Barnier said he is open to any discussion on the hot issue of the Irish border while confirming that about 90% of the Brexit deal issues have already been sorted out between the European Union and the UK.
While talk at Westminster is of the potential for a second referendum, MPs will consider the legitimacy of the 2016 plebiscite which resulted in the historic decision to leave the EU.
He also lashed out at the Northern Ireland "backstop" - the measure aimed at making sure there is no hard border with Ireland.