Mr Kenny clearly signalled that the Government would examine the wider implications for its role in future campaigns.
But he and Tanaiste Eamon Gilmore both dodged questions about Attorney General Maire Whelan's role in clearing the wording of the information booklet.
In the unlikely event of a shock No vote, the finger of blame can be expected to be pointed at Ms Fitzgerald and Ms Whelan for the leaflet debacle.
The Yes campaign feels that the potential threat to the referendum will galvanise support among people who might not have bothered to vote.
"Ironically, this will help turnout because people see this as too important to let it be defeated. People will be able to separate the two issues," a coalition TD said.
But there are concerns that it could affect the turnout, which is already expected to be low.
A minister said: "It's hard to say. It could increase the turnout because the campaign caught fire for the first time and this might cause Yes voters to come out for fear that it could be tight.
"At the same time, the court decision might have sown doubts among Yes voters who might stay away -- which would be a real shame."
The main political parties are all telling their TDs to do everything they can to ensure that their supporters turn out to vote today.
Fine Gael's director of elections, Leo Varadkar, wrote to all his party colleagues earlier this week. He said Fine Gael would be distributing a final 100,000 leaflets in an attempt to get out the vote.
Mr Varadkar wrote: "I would urge you to do everything possible . . . in terms of encouraging people to vote, in particular through a visible presence at supermarkets, town centres and transport stops."
The Labour Party also contacted all its TDs, senators, councillors and members of its executive council, urging them to contact their supporters.
"Notwithstanding the issues that arose in recent days, we are asking people to focus on the core reasons why this referendum should be passed," a spokesman said.
Mr Kenny indicated that a post-mortem would be held into the fiasco after the Supreme Court gives the reasons for its judgment on December 11.
Any post-mortem is likely to feature on the role of the Office of the Attorney General, legal advisers to the Department of Children and Youth Affairs, ministerial advisors and key civil servants, all of whom were involved in the preparation of materials for the website and booklet.
Mr Kenny dismissed calls for today's poll to be postponed in the wake of the Supreme Court's ruling that some of the information published was not "fair, equal and impartial".
"I'd like to look at the detail of the Supreme Court decision when it is actually published," he said.
"I think, arising from this, we need to reflect on the relationship between when government decides to put a question on a referendum issue to the people, the role and responsibilities of referenda commissions in the future, the role and responsibilities of government and how that should be dealt with for the future."