This might easily be an insuperable barrier, even if the PM isn’t
Let’s make the heroic assumption that the Tories are brought down in a Vote of No Confidence, Corbyn cannot gather the support to form a government but he reluctantly concedes that if someone else can, on a temporary basis, in order to secure an Article 50 extension and then trigger a general election, Labour will support that.
This is, frankly, a long shot. Corbyn has not sounded at all amenable to supporting anyone else and with enough people being even more opposed to Corbyn, there’s a good chance that a No Confidence vote would fail anyway as MPs sought to avoid falling into an election that delivered No Deal anyway, left parliament powerless to act and Remain voters extremely angry, including at the parties they assumed would stop it.
However, it’s a starting premise. Plenty of speculation’s been given over to alternative prime ministers during the last month, pushing Ken Clarke to second-favourite at 14/1 (it’s a sign of the times that Nigel Farage is joint-third-favourite with Keir Starmer at 16/1, and then Jo Swinson at 20/1; the shortest-priced member of the cabinet is Sajid Javid at 25/1).
The problem doesn’t end there though; indeed, it only begins. It’s all very well a Temporary Anti-No Deal Administration (i.e. a TANDA) existing solely for the purpose set out at the beginning of the article but the rest of government still goes on, and such an administration would be in office for over a month, during the election as well as the A50 extension negotiation. Decisions would need taking and policies determining. Clarke – or whoever – couldn’t do all of it. Such an arrangement might have worked for Wellington in 1834 (the only other genuinely caretaker administration), who appointed himself as the only Secretary of State and went from office to office transacting urgent business as he saw fit but the world has moved on and government is a more complex beast.
If Labour was prepared to accept, say, Clarke as a temporary PM, then presumably Corbyn would demand a high price in terms of other offices. After all, Labour has about 7 MPs for every 2 from the minor parties. A minimum bid might be perhaps Deputy PM for Corbyn, as well as at least two of the three other Great Offices of State, two of the three biggest spending departments (Health, DWP and Education), and the bulk of the lesser posts.
But it could be more than that. The SNP (almost half the remaining MPs) presumably wouldn’t accept office in a UK government; likewise Plaid. Would the ex-Change UK defectors in their various guises be happy to sit alongside so many Labour ministers? You’d assume not. Lucas might but what of the Lib Dems? Scarred by their experience in government with the Tories, they’ve already ruled out any long-term coalition; their natural position would be in giving Confidence from outside the government.
So what we come back to is very close to being a Labour government headed by a Tory and with at most a smattering of other odds-and-sods. Is that something that a Tory (presumably an ex-Tory by that point) could accept? Would such an administration be ungovernable given the power of Labour within it? For that matter, is such an obviously not-GNU something that Labour could support in that format once it became obvious that the other parties wouldn’t take part?
Perhaps the urgency and importance of Brexit would override all else – but then if so, wouldn’t an outright minority Labour government also do so? But I feel that far too much is being taken for granted on the assumption that agreeing on a PM automatically produces a government: that very much needn’t be the case.