It does look as though it will take a superhuman feat to pay for expanded higher education to cater for half of all school-leavers without alienating middle-class voters and driving away working-class students.
After endless inter-departmental wrangling, the long-awaited strategy paper on university funding has been put back to January. Top-up tuition fees are still Number 10's preferred way of injecting funds into top universities. The question is can Mr Clarke, unlike Estelle Morris, bring himself to support them?
The resignation of Ms Morris is said to have been caused partly by a bruising battle over top-up fees with Andrew Adonis, the Prime Minister's head of policy. Mr Clarke, a former president of the National Union of Students, said his initial feelings about top-up fees were "generally anti". But he added that it was important to introduce a broader range of students into the system and said his mind was not made up.
He may be reasssured by the fact that more help for poor students is on the way. A proposal to extend educational maintenance allowances of at least pound;40 a week to university students seems likely to go ahead, effectively heralding the re-introduction of student grants for the less well-off.
Some top universities, notably London's Imperial College have drawn up plans to charge up to pound;10,500 a year. At present, they cannot charge home students more than the standard pound;1,100. Other options include an across-the-board rise in tuition fees or a graduate tax.