So, with a UK led by Andy Burnham looking increasingly likely, what do political opponents in Scotland think?
The SNP have labelled him “more of the same” and “shallow and ego-driven”.
Privately, some SNP insiders concede that Andy Burnham does appear to be communicating more effectively. And – in the short term – could improve Labour’s fortunes.
But there’s a feeling that the fundamental challenges he faces are the same faced by Sir Keir, and that he’ll be largely constrained by the same economic conditions.
There don’t seem to be any Andy Burnham visits to Scotland planned.
Much of his focus at the moment will be on trying to retain the Greater Manchester mayoralty for Labour next month.
However, he is scheduled to meet with Scottish MPs later this week.
After a dismal showing in the Holyrood election last month, he’ll have to convince them that he has a plan to rebuild north of the border.
Selling that message to those MPs is one thing – that’s an audience who will want him to succeed.
If he reaches Downing Street, he’ll then have to sell it to the Scottish public. Who may well prove to be a bit more sceptical.