Today, only a week after she took up her new post, Ms Kelly is handed a warning that a clear majority of heads want the Tomlinson report on 14 to 19 qualifications implemented in full.
Tony Blair insisted in October that A-levels and GCSEs would remain despite the report's proposal that they should be replaced by a diploma. Ministers are also nervous about the radical recommendation that traditional, externally-assessed exams would cease for most teenagers until the age of 18.
But an end-of-term TES poll taken before Ms Kelly responds to the report in a White Paper next month, reveals that seven out of 10 secondary heads want to see GCSEs and A-levels replaced by the diploma framework proposed by the former chief inspector.
The report by Mike Tomlinson, the former chief inspector, is the most urgent item in Ms Kelly's in-tray and she has been briefed on its contents by civil servants. She is likely to face tough questions when she delivers her first major education speech at the North of England conference in Manchester next month.
The TES poll shows that, of three options: retain the current system; implement a compromise in which the names "A-level" and "GCSE" are kept; or the Tomlinson diploma in full, 66 per cent favoured the latter. Only 15 per cent opted for the status quo and 20 per cent for the compromise option, which the Government appears to favour. The poll is based on returns from 102 heads over the past week.
Paul Griffiths, head of St Clere's, in Thurrock, Essex, said: "We have to move beyond the current system. Tomlinson has correctly judged the mood in education."
Lawrence Montagu, head of St Peter's Catholic high, Gloucester, said:
"People who try to negate the work of Tomlinson are just trying to turn the clock back to the 1970s, or before. Simply arguing that we cannot change is not an option."
Charles Clarke, Ms Kelly's predecessor, said league tables and external exams at 16 would stay.
Ministers appear, however, to be ready to implement many of Tomlinson's less contentious suggestions, including an improvement in vocational courses designed to increase England's low staying-on rates and basic maths and English for the over-14s.
Even these, however, carry risks for Ms Kelly and her department.
Chancellor Gordon Brown could take fright at the cost of hundreds of thousands more over-16s staying in education and training. This week, Mr Brown was warned he may have to raise taxes by pound;10 billion because higher-than-expected public spending this year has left a shortfall in the nation's finances.
Mr Tomlinson said of the poll: "The Government should take note of the views of practitioners."
But John Claydon, head of Wyedean school, Gloucestershire, said: "I'm astonished that there is apparently so much support for this wishy-washy plan."
Teachers' leaders are concerned that the plans could add to their members'
workloads but all unions are broadly in favour of Tomlinson.
Research by Patrick Hayes news 3, Leader 14