The rights came into effect yesterday, with the bizarre consequence that parents of any baby born before midnight on Tuesday were not eligible. In labour wards up and down the land you could hear midwives shouting: "Don't push!" or "OK, the baby's head is out. Now, could you just hang on like that for another 47 minutes?" In the case of twins born either side of midnight, I suppose the parents get the statutory 13 weeks' leave. But to stay within the spirit of the law, they should make an effort not to bond with the older one.
The legislation is part of the Government's very laudable plan to get fathers more involved with the care of their newborn children. But the question that is on everyone's lips at Westminster is: will the man who made this legislation possible take advantage of it himself?
Of course, the Prime Minister will be there at the birth of his fourth child, encouraging Cherie to "meet the challenge of the new millennium". But then what? Will he go back to work himself?
Most men like to make out that their job is really important, and as Prime Minister, Tony Blair does possibly have a case. But he would be contradicting all the Government's messages about parenting if he did not at least take some time off work. It is not as if he does not have complete confidence in his deputy, John Prescott, to take on more responsibility than he has at the moment. Ahem.
What will make it harder for Mr Blair is that not only does he work at home, but even if he did try to take some time off, ministers would still keep coming round to his house, stepping over the buggy in the hallway to have meetings in the Cabinet Room. How is Tony supposed to ignore that? With the baby in his arms, he would put his ear to the door and hear all the Old Labour tendencies resurfacing without him.
"So that's agreed then, we'll renationalise all the public utilities without compensation to shareholders" - and then Tony will tentatively put his head around the door.
"Oh, hi, Tony!"
"Sorry, did I hear something about re-nationalisation?"
"Oh, don't worry about any of that. You carry on looking after the baby. See you in 13 weeks."
"Right, um. Nothing I can help with?"
"Tony, I think that Babygro looks like it needs changing."
The other alternative is for Tony to take the baby to work with him. Nothing could be more disarming than a party leader standing at the dispatch box with a little baby wriggling in his arms.
The angry hostility of Prime Minister's Questions would evaporate overnight.
"Madam Speaker, is the Prime Minister aware that his new baby is really, really lovely and looks just like his dad?"
"Madam Speaker, this may be the case, but I think that if the honourable members opposite were to look at the photos of our babies born under the last Conservative government, they would find they looked much more like their mum."
When there is a baby present, it completely takes over as the focus of attention in the room. A shadow minister might deliver the most damning speech on government policy, with shocking statistics, brilliant quotes and a blistering personal attack on the Prime Minister. But while the baby is trying to grab Madam Speaker's little finger, no one is going to take the slightest bit of notice. With a bit of training it could probably even learn to be sick every time John Redwood starts speaking.
Foreign heads of state will have to meet the Prime Minister when he is free, namely at half-past three in the morning when it is his turn to get up. The weekly audience with the Queen may lose some of its formality. "Can you just take that dirty nappy out to the wheelie-bin please, your Majesty. Baby's just gone and wee-ed all over the changing mat." Frankly it's very hard seeing the Prime Minister doing any of this. He cannot just give up work, yet he cannot be seen not to set an example. So there can be only one foreseeable outcome.
Although pregnancies are generally 40 weeks long, soon we can expect an announcement that the Government cannot find the time for the birth of the baby during the next parliamentary session, and that it cannot be delivered this side of the general election. It may seem a bit hard on Cherie, but the homeless and the unemployed have had to learn to wait for Labour promises to be delivered. Cherie will just have to hold on as well. Women used to go into labour after nine months. New labour takes a little bit longer.
John O'Farrell is the author of `Things Can Only Get Better' (Black Swan, pounds 6.99)