A ministerial resignation statement on a Wednesday would normally follow Prime Minister's Questions, but friends of the former foreign secretary are predicting the government will stage at least one ministerial statement after PMQs so Mr Johnson does not immediately follow Theresa May.
The amendment would have forced the Government to adopt a negotiating objective of seeking to keep the United Kingdom in "a customs union" with the EU after Brexit, unless it has managed to negotiate a "frictionless free trade area for goods" by next January.
May was defeated, however, on a separate amendment about medicine regulation.
On two of Monday's votes her majority was cut to three, suggesting that the leader will struggle to get Brexit legislation through a deeply divided parliament, which could possibly threaten the approval of any Brexit deal with the EU.
Pro-EU lawmakers have tabled a change to the wording of the bill to try to force the government to pursue a customs union with the EU if ministers fail to reach an agreement which establishes "a frictionless free trade area for goods".
Britain's European Union membership was critical to United States interests, with the policy underpinning the agenda of all UK governments since Britain entered the European Union in 1975.
But in a separate blow for the PM, she was defeated on an amendment which calls for the United Kingdom to stay in the European medicines regulatory network, losing by 305 to 301.
But Mrs May suffered a setback when another rebel amendment, seeking to keep the United Kingdom in the European Medicines Agency, was passed by the Commons. Near miss on customs union amendment.
Netflix's share price slumps 14 per cent after disappointing second quarter
While most of the company's revenue growth comes from global markets, the vast majority of its costs remain dollar-denominated. Apple, the world's most valuable company, is spending about $1bn on original programming for a video service of its own.
The Green Party MP Caroline Lucas said the vote would strengthen calls for a second European Union referendum on the terms of the UK's Brexit deal. It said it objected to the amendment because it requires the government to take "all necessary steps" to join, while the government wants to join only if it can negotiate reasonable terms.
In the afternoon Mrs May faces a lengthy appearance before the Commons liaison committee where senior MPs of all parties will grill her on her Brexit strategy. Any final deal with the European Union will also require ratification by a bitterly split parliament.
12 Remainer Tory MPs rebelled against the party whip: Heidi Allen, Guto Bebb, Ken Clarke, Jonathan Djanogly, Dominic Grieve, Stephen Hammond, Dr Philip Lee, Nicky Morgan, Robert Neill, Antoinette Sandbach, Anna Soubry, Dr Sarah Wollaston.
"Theresa May is in a more hard position than I was", he told ITV News.
Mrs May narrowly avoided a defeat in parliament at the hands of the pro-EU members from her own party in the vote.
Will Boris Johnson take the opportunity to attack Mrs May's Brexit plan? Sir Jeffrey Donaldson said: "We are very content for Parliament to meet next week on Monday and Tuesday and had planned accordingly".
"That would have looked too much like plunging the knife into the prime minister", a close ally told Sky News.
Shadow Scotland Secretary Lesley Laird said the fact that no Scottish Conservative MPs rebelled against the government meant "Ruth Davidson's pledge that her MPs would stand up for Scotland was nothing short of a lie".