Opposition leaders failed to agree on the timing of a vote of no confidence when they met earlier this week, delaying any bid to oust Mr Johnson from Downing Street, and the parties failed to secure any emergency debates to put pressure on ministers over Brexit this week.
Frustration boiled over last night, with sources in the SNP and the Liberal Democrats mounting a briefing against each other.
The SNP is pushing for a swift election, while Labour and the Lib Dems want to wait until legislation delaying the UK’s Brexit date takes effect on 19 October.
The parties are also at odds over whether to allow Jeremy Corbyn to lead a caretaker government of national unity that would request a delay from Brussels and call an election, with Lib Dem leader Jo Swinson standing firm against letting Mr Corbyn into No 10.
“There is a deep sense of frustration in the SNP that the cross-party meetings aren’t going anywhere, that no meaningful action is being taken, and there is a concern that Brexit could end up happening because of a failure of leadership,” a Nationalist source said.
“The SNP has presented their plan but the Lib Dems are acting as a roadblock and no credible alternative has been presented. What started as a constructive process that achieved results is going nowhere.”
A Lib Dem source hit back: “The only people who currently think a vote of no confidence is a good idea are the SNP and Boris Johnson.
“They are putting their desire for an election above what is good for the country, which is a totally reckless course of action.
“A vote of no confidence now would make no-deal more likely, not less, which is why the other opposition parties have agreed it is not the best course of action right now.”
Meanwhile, at Prime Minister’s Questions, the SNP’s Westminster leader Ian Blackford made a public call for opposition parties to unite and “bring this dangerous government down”.
He urged opposition MPs to “step up at this moment of national crisis” to “prepare a vote of no confidence, ensure a Brexit extension, prevent a no deal and call a general election”.
Mr Blackford said: “This government must be stopped. I’m looking now at colleagues on opposition benches and I urge them we must unite, we must stop this Prime Minister by removing him from office.
Standing in for Mr Johnson at PMQs, Foreign Secretary Dominic Raab accused Mr Blackford of “sounding like he’s all mouth and no trousers”.
Mr Raab added that “he had the chance to vote for a general election and he turned it down, he had the chance to avoid no deal and the best chance now is to back this government in securing a good deal”.
Referring to the government’s fresh Brexit proposals, Mr Blackford said Mr Johnson’s “Brexit fantasy” was an “unacceptable” deal and “doomed to failure”.
He said: “Is this government seriously planning to take on Parliament in the courts to force through a catastrophic no-deal Brexit or will the Foreign Secretary now rule that out?”
Mr Raab replied: “Of course this government will always adhere to the law... we want to take forward the negotiations, we want to avoid a no-deal scenario and actually rather than undermine the negotiations in Brussels, I’d urge the SNP to try and support the government in securing a deal which is good for this country.”
Mr Raab called on the SNP to respect the “judgment of the people of Scotland when it comes to staying in the UK and the judgment of the people of the UK to give effect to the referendum on the EU”.
The SNP has been urging Labour and the Lib Dems to agree on a compromise candidate to lead a national unity government following a vote of no confidence.
But with Labour insisting that the candidate has to be Mr Corbyn, and the Lib Dems and Conservative rebels implacably opposed, the talks have made little progress.
Mr Blackford told BBC Radio Scotland: “I do think there is a danger we run out of time, because when we call a motion of no confidence we have 14 days to put an administration in place. Once we get to the middle of October the options for us are beginning to close off.
“Everyone has to accept their responsibility. We are willing to do our part to bring Boris Johnson down - why are the other parties not prepared to do what is necessary to remove this man from office?
“We are not prepared to sit back and let Scotland be dragged off the cliff edge by Boris Johnson.”
He said allowing a no-deal Brexit would be a collective failure by the opposition.