Jeremy Corbyn says "he's taking us away from Europe into the arms of Donald Trump by his obsession with a no-deal Brexit".
Independent Group for Change leader Anna Soubry told the BBC Radio 4's Today programme on Thursday that she would not "support a government of national unity" led by Mr Corbyn "for all manner of reasons".
Welsh Conservative reaction to Mr Corbyn's letter was scornful, with Monmouth MP David TC Davies tweeting that the plan was like "a coup d'etat of the sort favoured by Marxist dictators in banana republics from whom he draws inspiration". The new minority Labour government would then extend the Brexit process to create time for a general election.
Yesterday he said those trying to block Brexit were engaged in "a awful kind of collaboration", after former finance minister Philip Hammond said parliament would block a no-deal exit, and that the government must respect it.
"And our European friends are not moving in their willingness to compromise, they're not compromising at all on the Withdrawal Agreement even though it's been thrown out three times, they're sticking to every letter, every comma of the Withdrawal Agreement - including the backstop - because they still think Brexit can be blocked in Parliament". They fear that after Brexit, the government will erode workers rights, weaken environmental and other standards and row back on the welfare state.
Mr Kwarteng said: "I don't see Jeremy Corbyn being able to come together with the numbers, nor do I see any prospect of him leading a so-called national unity government".
"I look forward to joining her in the lobbies to vote this Government down".
The Labour leader said that "it's not up to Jo Swinson to decide who the next prime minister is going to be" after she swiftly dismissed his proposal to force a general election as "nonsense".
The prime minister has a working majority of just one in the House of Commons, with the backing of Northern Ireland's Democratic Unionist Party.
Mr Corbyn said Mr Sedwill's response to him on Tuesday had been "non-committal" but should inform discussions with other parties.
Ms Swinson said she was ready to "work with anyone" to stop Mr Johnson and his "hardline Brexit Government".
Meanwhile, Boris Johnson and his Vote Leave colleagues continue to run down the clock in the expectation that Brexit will happen by default.
He would then seek an extension to the Article 50 process to delay the United Kingdom leaving the European Union past the October 31 deadline.
He added: "'This government believes the people are the masters and votes should be respected, Jeremy Corbyn believes that the people are the servants and politicians can cancel public votes they don't like".