A Christmas card bearing the father-to-be's face will be taken to Downing Street on 15 December, when the new European parental leave directive comes into force.
Parents of children born after that date, including the Prime Minister and his wife, will be entitled to take 13 weeks' unpaid leave before the child's fifth birthday. The Manufacturing Science and Finance union (MSF) complains that millions of parents of young children will miss out because of the cut-off date. The union is organising a delegation of parents to deliver the card to Mr Blair.
Roger Lyons, general secretary of MSF, believes the Government has "failed" working parents and he described the cut-off date as "arbitrary and unfair". He said: "The parental leave directive is a big step forward in creating a family-friendly workplace, but excluding so many people from the new rights isn't very friendly at all."
The union also argues that under the original European directive it should be available until the child is eight.
It also wants organisations to be required to keep records of leave taken. "Bad employers could take advantage of that by insisting that employees had taken leave when they hadn't," Mr Lyons said. The union, one of the Labour Party's biggest affiliates, claimed that pressure from employers' groups, including the Confederation of British Industry, had led to the directive being diluted.
The amount of leave in any one year has been restricted to four weeks, although businesses will be able to adopt their own systems.
Ministers have extended the availability of leave to the parents of disabled children until the child's 18th birthday. A spokeswoman for the Department of Trade and Industry, said 15 December was chosen because that was the deadline for the introduction of the law set by the European Union.
Asked why any cut-off date was imposed, she said it would ensure that demand for leave built up slowly and the "goodwill of employers is maximised".
She said that the fifth birthday of the child was used because that was when he or she started school.