These reactions reflect what are no doubt genuine fears about his likely appeal to the wider electorate - though, unexpectedly, the polls show he is now the most popular of the candidates, not just with Labour voters, but with voters generally.
What is surprising, however, is that the critics focus on the supposedly extreme nature of Corbyn's policy prescriptions, especially in the realm of economic policy. Yet, as 40 reputable economists have declared this week in an open letter, Corbyn's economic policy may be at odds with current orthodoxy but is really no more than common sense.
It seems, for example, that - shock, horror - Corbyn and his advisers do not believe that austerity is the proper or effective response to recession. This is more or less the position reached by the IMF and endorsed now by a growing number of (in some cases, Nobel Prize-winning) economists. It is in essence no more than mainstream Keynesian economics. We can see the consequences of its rejection in the problems faced by an austerity-ridden eurozone.
Corbyn also takes issue with the peculiarly British version of austerity - the insistence that the wealthy should be spared, with the help of tax cuts and quantitative easing, from taking any responsibility for recovery, while the burdens are heaped instead on the most vulnerable, whose job prospects and living standards have taken huge hits.
Corbyn seems to assert, reasonably enough, that a serious effort to bring about a sustainable recovery requires that every shoulder should be put to the wheel.
A Corbyn Government would also recognise, it seems, that there might actually be a case for government playing its proper role in achieving a fair, balanced and productive economy. It's enough to make the blood run cold. Yet, surely, it makes sense for a government to use - alongside the private sector - its powers and resources to do the things that the private sector cannot, or, at least, will not, do.
Corbyn asks, why is quantitative easing fine when used to bale out the banks yet not for investment in new productive capacity and jobs? The fact that questions and policies such as these create so much alarm and despondency among Labour's erstwhile and would-be leaders tells us more about them and the state of the party than it does about the merits of the policies themselves.
The Corbyn economic policy platform, in other words, is comfortably in line with what is fast becoming the new consensus - less doctrinaire and more common sense than the old orthodoxy. Whether these factors will actually produce a Corbyn leadership remains to be seen, but he has certainly revitalised the party and enthused potential Labour voters. By opening up a long overdue debate, he has redefined the political landscape and offered new hope to those who have been conditioned to believe that "there is no alternative".
Labour leaders elsewhere, not least in New Zealand, will - or should - be watching closely.