The House of Commons will debate changes to the laws of royal succession today.
The legislation would end discrimination against female royals so that men no longer took precedence over women in the order of succession.
That would mean the Duke and Duchess of Cambridge's first child can become monarch even if it is a girl who later has younger brothers.
The proposals will also end the bar on royal heirs marrying Catholics if they want to keep their entitlement to the throne.
Deputy Prime Minister Nick Clegg has been warned that Government plans to change the laws of royal succession will put future monarchs in the "invidious" position of having to decide whether to veto the marriage plans of their children and grandchildren.
Appearing before the committee, the Deputy Prime Minister faced criticism for the Government's plans to rush the Succession to the Crown Bill through the House of Commons in a single day.
Former Attorney General Lord Goldsmith said plans to fast-track the legislation were "worrying", while Lord Crickhowell said he was "concerned" that Parliament was not being given enough time to secure satisfactory answers from ministers about the changes they are proposing.
A member of the House of Lords Constitution Committee also warned that the lifting of a historical ban on heirs to the throne marrying Catholics could bring into question the Church of England's position as the established church.
Government plans to change the rules on succession to the throne have been cleared by Buckingham Palace, David Cameron told MPs today.
Mr Cameron said:" What I can say is throughout the process of bringing forward this proposal, which is a proposal that head of all the Commonwealth dominium realms have also signed up to, through that process there has been thorough contact between Number 10 Downing Street and the Palace.
"All of the issues are settled and agreed."
Father of the House Sir Peter Tapsell had queried whether the plans - which will allow first born women to take precedence in the line of succession for the first time and allow marriage to Catholics - were backed by the Royal Family.