Peter Dunne probably has more chance of winning Lotto than securing a majority in Parliament for his bill allowing income-splitting to become law - at least in the measure's current shape.

The United Future leader knows he is up against it. That was evident yesterday when he challenged other parties which applauded themselves as being family-friendly to back it.

Having told politicians from other parties to put up or shut up, he promptly went over their heads and appealed to the public to put pressure on MPs to support his bill.

In short, the bill would allow couples with children to combine their incomes for tax purposes and then split the total in two halves, thereby paying a lower amount of tax by avoiding the higher rates paid on the larger income.

Having castigated National's tax cuts as favouring the rich, Labour can hardly endorse a scheme which would have some well-heeled couples pocketing more than $9000 in tax refunds.

Government ministers have exhibited about as much enthusiasm for National's support partner's measure as that shown by Labour.

If he did have a spare $450 million - the cost of Dunne's scheme if there is maximum take-up - Bill English has more pressing priorities.

On top of that, there is always the strong view within the larger partner in any governing arrangement that it has the monopoly when it comes to determining something as fundamental as tax policy.

While such a measure might go down well with many of National's core supporters, the party leadership will be acutely conscious that many middle-income earners would not benefit because it would not move part of their income from a higher marginal tax rate to a lower one.

Where National has come to the party is in honouring the provision in its 2008 confidence and supply deal with United Future for income-splitting legislation at least to be given a first reading and be sent to a select committee.

With the five Maori Party MPs also on board, Dunne's bill is now guaranteed to get that far.

At a minimum, the select committee hearings will serve as a valuable branding opportunity for the one-MP party.

Dunne faces huge obstacles to his bill making making further progress in the House, however. The first is time. The bill may not be reported back to the House before February next year. The number of days that Parliament sits in election year is necessarily less than normal. National could let the bill wither on Parliament's order paper until the election, thereby avoiding having to make a decision on it, though probably not a dust-up with Dunne.

One option - but one with still only a very outside chance of success - would be for Dunne to manoeuvre a compromise which might restrict income-splitting to couples with children under a much lower age than the current limit of 18 listed in the bill.

Dunne's seemingly insurmountable problem is National and Labour's dominance of the House. One course of action could see the pair killing the bill at the select committee stage.

That would be in the interests of both. Better to cop any public backlash together, rather than one of them copping it all separately. You might call that opprobrium-splitting.