Senior Tories said dividing the £200,000-a-year post of clerk into procedural and management positions is a "grubby compromise" that fuels rather than eases concerns about the decision to bring in Ms Mills.
Speaker John Bercow has been under intense pressure over the decision to open up recruitment for the job, which combines the constitutional role of clerk of the House of Commons with being the chief executive responsible for running the building and almost 2,000 staff.
Concerns have been raised about Ms Mills' ability to carry out the procedural side of the role, with former speaker Baroness Boothroyd warning she would be "totally out of her depth".
It emerged yesterday that parliamentary lawyers are understood to have found a way to allow the post of clerk to be divided into two.
Bernard Jenkin, chairman of the Public Administration Select Committee, said: "The announcement it is intended to split the roles of clerk and chief executive ... is tacit admission that the appointment may be far from ideal."