And pressed on whether he would quit if he was unable to take the UK out of the EU on 31 October, the prime minister himself said only: “That is not a hypothesis I am willing to contemplate.”
Speculation over a possible resignation was fuelled when Mr Johnson said on Thursday that he would rather be “dead in a ditch” than go to Brussels to ask for an extension to Brexit negotiations.
Legislation due to complete its passage through parliament on Monday will require him to do this unless he has first secured a Brexit deal or parliamentary approval for no-deal.
Mr Johnson is expected to fail on Monday in a second attempt to trigger a general election on 15 October, with opposition parties planning to reject the proposal, which requires a two-third majority in the House of Commons.
The PM and his advisers believe that a snap election would allow him to obtain a Conservative majority large enough to vote through a no-deal outcome if no agreement is reached at a crunch Brussels summit on 17 October.
But Labour, Liberal Democrats and other opposition parties are thought to have agreed to withhold their support for a poll until after the PM has requested an extension to the UK’s Brexit deadline to 31 January.
A Downing Street spokeswoman was asked at a regular Westminster media briefing whether Mr Johnson’s comments indicated he would resign rather than request an Article 50 extension.
She replied: “I think that the PM has made his position on extension clear a number of times this week. In relation to MPs and the decisions that they are facing, the PM has said that the current position is unsustainable and that MPs should consider over the weekend whether they are prepared to face up to the consequences of their actions this week in passing a bill that wrecks our negotiations and seeks to impose an indefinite delay to Brexit.
“He has been very clear that they must take responsibility for their actions and face the public in a general election, and MPs will have a chance to do that on Monday.”
Asked directly whether she could rule out Mr Johnson resigning, she replied: “We are taking one step at a time here and the next step is for MPs to consider over the weekend the decision they will take on Monday.”
Pressed on whether Mr Johnson accepted that even if he were to resign, he would have to remain as prime minister until a successor was appointed – potentially after the 31 October deadline has passed – the spokeswoman said: “I appreciate the question, but you are getting three or four steps beyond where we are now. The situation you are putting to me is a situation which hasn’t occurred.”
Mr Johnson dodged the question of resignation during a visit to a police training academy in Yorkshire on Thursday.
In response to a question on whether he could promise not to ask for an extension to Brexit negotiations, the prime minister replied: “Yes, I can. I would rather be dead in a ditch.”
But challenged on whether he would therefore resign if the bill becomes law on Monday, he simply repeated his objection to an extension: “It costs £1 billion a month, it achieves nothing. What on Earth is the point of further delay? I think it’s totally, totally pointless.”
A Number 10 source insisted earlier this week that the PM would not stand down if parliament required him to extend Brexit negotiations.
“He is not going to stand down,” the source told reporters on Wednesday. “We will find a way to deliver on what the British people want, which is to deliver Brexit on 31 October.”
It is not clear how Mr Johnson could avoid asking for an extension if Hilary Benn’s bill becomes law, other than by striking a deal with Brussels, resigning or breaking the law.
Asked in the House of Commons on Tuesday whether the government would abide by the rule of law if the bill makes no-deal illegal, Mr Johnson told MPs: “We will of course uphold the constitution and obey the law.”
The cabinet’s no-deal supremo Michael Gove told a Commons committee on Thursday that the government would obey the law, but could not explain how this could be reconciled with the PM’s refusal to ask for an extension.
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