While he would surely disagree, that burning issue is nothing to do with Covid, Brexit or the energy price crisis. Instead, it is whether he is capable of turning Labour into an effective opposition or whether it will remain bogged down in internal bickering until defeat at the next general election.
The Labour leader appears to be a capable, intelligent and caring individual, but he may lack the charisma to overcome Labour’s age-old ideological struggles and the unrealistic stances taken by some on his party’s left.
Writing in the i newspaper, former Labour leader Jeremy Corbyn accused the Labour leadership of wanting to “prop up, not challenge... wealth and power. There is another way forward, that is based on social justice, and in the policies the majority of people actually want, not what the establishment and its media mouthpieces insist they should want.”
Since 1979, Labour has won three general elections, all with Tony Blair in charge, and lost eight, including two when Corbyn was leader, so his idea of what “majority of people actually want” appears to be more a product of his imagination than anything else.
One of the most contentious issues at the party conference has been whether the minimum wage (currently £8.91 for those 23 and over) should be increased to £15 an hour. Why Labour should be tearing itself apart over this when it is not in power, the next general election is years away, and such conference votes are not even binding is hard to fathom.
But what should be obvious to all is that if Starmer cannot even unite his own party, he has little hope of putting together a sufficiently large coalition of voters to have a fighting chance of beating the Conservatives.
And that should worry unionists in Scotland because one of the main driving forces behind recent strong levels of support for independence has been the exodus of left-wing voters from Labour to the SNP as they give up on the idea that the UK can be a social democratic country.
So there is more riding on Starmer’s speech than it might first appear.