Mr Blackford, leader of the 35-strong SNP group in the House of Commons, accused some of those fighting to avoid a no-deal Brexit of 'failing to recognise the challenge' of leaving the EU without an agreement in place at the end of the month.
There have been splits among Labour, Lib Dem, and other opposition politicians about who could become Prime Minister in order to send the EU a letter requesting an extension to the Article 50 process.
Liberal Democrat leader Jo Swinson has insisted that her party could not countenance putting Labour leader Jeremy Corbyn in Downing Street, saying that he doesn't command enough support and is not as clearly opposed to Brexit as those in her party.
Mr Blackford told the BBC's Good Morning Scotland:
"The opposition parties have worked well together and all supported the Benn Act which forbids a no-deal Brexit at the end of the October.
"The challenge that we face is that we've got a Prime Minister who will stop at nothing he's still threatening to leave on a no-deal Brexit despite that being unlawful.
"I would say that if we want to guarantee that Boris Johnson is not going to try and take us out on a no-deal basis then we have to take the keys of No10 away from him.
"We need that motion of no confidence, we need to put someone in on a caretaker basis, that will write the letter extending Article 50 then we will have an election.
"I say to colleagues if we fail to do this,. then there is a risk that Boris tries to crash out and that will be a failure of leadership."
The Skye MP insisted that the SNP is not being 'precious' about who takes over from Boris Johnson in the event of a successful vote of no confidence, and said appointing a new Prime Minister was an 'administrative function' to prevent no-deal.
He added: "I'm asking everyone across all the parties including the rebel Tories, to recognise the challenge in front of us and to go the extra mile.
We're all going to have to compromise as to who that candidate will be. We're willing to play a constructive part in that the others will have to compromise too.
"We're happy to look at any candidates. Jeremy is the leader of the opposition and there has to be a prospectus that he can command a majority.
"It may be that he can't and we have to coalesce around another individual, and we're not being precious about who that is.
"We're willing to work with others, its up to others to work with us to take this toxic Prime Minister out of office."