I would trust Jeremy Corbyn as far as I can throw him. So I am pleased that Jo Swinson has said the Lib Dems will talk to Labour but not support Corbyn's appointment as Prime Minister. The last thing we should be doing as a Remain party is to put a Leaver in the driving seat. Corbyn doesn't even command the support of the bulk of his MPs. A National government will need the support of some Conservative MPs. Corbyn will kill off any idea that a good size group of Conservative MPs will back a National government. But it could be possible for enough MPs from across the political spectrum to come together to back a government led by a senior Labour or Conservative figure. Today, the names of Harriet Harman, Ken Clark and Hilary Benn have been mentioned as possible Prime Ministers.
We are running out of time to sort all this out. Corbyn setting out to be PM will waste much of the little time we have left. The Lib Dems will support a no-confidence motion (we were calling for it before the recess but Corbyn sat on his hands). Corbyn says other opposition parties need to make compromises but he seems reluctant to follow his own advice by backing a Harman or Clark or Benn PM.
Nor are Corbyn's claims that he must be considered for PM as the leader of the 2nd biggest party. When the Labour government collapsed in 1931, Ramsey MacDonald continued as Prime Minister but not as Leader of any party (he was expelled from Labour). Conservative leader Stanley Baldwin had the 2nd largest number of MPs but did not take on the Premiership. Likewise, in 1940 when Chamberlain resigned as PM, he continued as Conservative leader even though Winston Churchill had become PM.
Both MacDonald and Churchill took over the reins of government without leading political parties but able to command a majority of MPs in the Commons. Corbyn cannot do that even as Leader of the Labour party. But, of course, this is not about Brexit as far as he is concerned. This is about getting the keys to Downing Street.