The Labour leader had written to party leaders and senior MPs asking them to support him in order to oust Boris Johnson and extend Article 50 but crucially, the Liberal Democrats rejected the plan.
Tory Remainer Dame Caroline Spelman and the Independent Group for Change also signalled they would not be on board, but other recipients of the have said they could support it.
SNP leader Nicola Sturgeon told Lib Dem leader Jo Swinson that she should rethink her rejection of the proposition, which the Lib Dem leader described as "nonsense".
Ms Sturgeon signalled her 35 MPs could support Mr Corbyn's plan for a no-confidence vote, extension to the Brexit deadline and general election with him as temporary PM.
In the letter - addressed to senior MPs including Ian Blackford, Jo Swinson, Liz Saville Roberts and Caroline Lucas - Mr Corbyn says he intends to "to table a vote of no confidence at the earliest opportunity when we can be confident of success".
He says his next step will be to "seek the confidence of the House for a strictly time-limited temporary government" before asking the EU for a Brexit extension which would allow time for a general election.
He told the politicians: "Our priority should be to work together in Parliament to prevent a deeply damaging no deal."
Three less of the less senior politicians to receive the letter - Nick Boles, Dominic Grieve, Oliver Letwin, Caroline Spelman - responded, saying they "welcome" Mr Corbyn's invitation.
In the collective reply, the MPs said: "We agree that our common priority should be to work together in Parliament to prevent No Deal Brexit and welcome your invitation to discuss the different ways that this might be achieved.
"We would be happy to meet with you as well as colleagues from other opposition parties whenever convenient in the weeks before Parliament returns."
And SNP Westminster leader Mr Blackford backed the no confidence move - and Plaid Cyrmu's Ms Saville Roberts said she was open to a unity government.
Greens leader Ms Lucas also said she would back a no-confidence vote, but added that she wants Mr Corbyn to guarantee Labour's support for another MP to lead a temporary Government if his bid to govern fails.
In response, Mr Corbyn tweeted: "Encouraging that MPs from across parliament have responded positively to our plan to stop No Deal. We must work together to stop No Deal and let the people decide the future of our country."
But Liberal Democrats leader Ms Swinson dismissed Mr Corbyn's request for support, saying "there is no way he can unite rebel Conservatives and Independents to stop Boris Johnson."
While Downing Street criticised him for planning to "overrule the referendum".
In her first major speech as Lib Dem leader, Ms Swinson said the Commons needed to win a vote of no confidence against Boris Johnson and within 14 days install a new PM who has "the confidence of the House and will stop a no-deal Brexit"
Instead she suggested "someone like Ken Clarke or Harriet Harman" to lead a temporary government.
Ms Swinson, referencing Mr Corbyn's suggestion, said: "He is demanding the keys to Number 10 as a precondition for a vote of no confidence.
"We are facing a national crisis. We may need an emergency government to resolve it. But if Jeremy Corbyn truly wants that to succeed surely even he can see that he cannot lead it."
She added: "Someone like Ken Clarke or Harriet Harman - the Father and Mother of the House - they are hugely experienced and, unlike Jeremy Corbyn, or indeed myself, they are not seeking to lead a government in the long term."
Former attorney general Dominic Grieve appeared to agree with the Lib Dem leader, saying "a government of national unity doesn't have to have a leader of any political party as its head".
However he did say he and colleagues were "entirely serious" about talking to Mr Corbyn.
He said: "If we wants to talk to us about stopping a no-deal Brexit, I'm perfectly prepared to speak to him, as are my colleagues."
Although he added: "Putting in a caretaker prime minister must be for some useful purpose. My impression from the letter he's written to me is that he wishes to be a caretaker prime minister to trigger an election.
"The difficulty is that an election in itself doesn't help solve the crisis in relation to Brexit. After an election we may still be in exactly the same crisis so I'm not sure that that's necessarily the best way forward."
Labour frontbencher Angela Rayner responded to Ms Swinson's remarks, saying she "does not get to choose who the leader of the Labour Party is".
Ms Rayner said: "Our leader is Jeremy Corbyn and she should respect the party and respect his title as the official leader of the opposition."
She added: "We are the biggest opposition party, she should work with Jeremy Corbyn - this is party political game scoring."
And Labour MP Tulip Siddiq criticised the Lib Dem's apparent reluctance to work with Labour, writing on Twitter: "The Liberal Democrats were willing to get into bed with the Conservatives for five years, but won’t join with Labour to prevent No Deal?! Are they for real?"
If Mr Corbyn is to succeed in calling a general election, he says Labour would campaign for a second referendum on EU membership with the option to Remain being available to voters.
Mr Corbyn will hope that the promise of his government only being temporary will be enough to secure the support of his critics who otherwise want to halt a no-deal.
In his letter Mr Corbyn says he wants to "halt the serious threat of No Deal, end the uncertainty and disarray, and allow the public to decide the best way ahead for our country".