OTTAWA -- The federal election is still five months away, but the Liberals and the Conservatives are already exchanging blows over their duelling promises of family tax relief.

Last week, Liberal Leader Justin Trudeau introduced a family-friendly plan -- part of the backbone of the party's forthcoming campaign platform -- that seeks to stake a claim squarely on the populist, low-tax territory coveted by the Tories.

So the Conservatives are countering with an offensive designed to blow holes in the math behind the Liberal child-benefit proposal -- a plan that abandons Stephen Harper's universal child care benefit.

The Tories have released updated government numbers that appear to indicate a $900-million shortfall in Liberal projections for next year -- a result, the Conservatives say, of the Liberal failure to account for the benefit's taxable status.

The Liberals insist any revenue lost as a result of ditching the universal child care benefit has been accounted for, and say they used publicly available figures to cost their family plan and to reach their inflation assumptions.

In an email, Trudeau spokeswoman Kate Purchase said the Finance Department numbers "are underestimating" the cost of an existing program that would be replaced by the Liberal plan.

It's an early preview of what are sure to be countless rhetorical skirmishes over economic assumptions, estimates and calculations that will erupt on the pre-campaign trail between now and the fall election, scheduled for Oct. 19.

During question period Tuesday, Trudeau repeated the Liberal accusation that the Harper government's family measures unfairly benefit the most wealthy Canadian families.

"Fairness means helping those who need help the most, so why not cancel those tax breaks and benefits that go to the wealthiest Canadians?" Trudeau asked.

The Liberals would scrap important programs, Harper retorted, before taking a swipe at Trudeau's arithmetic.

"Even after he takes all those things away, his numbers still don't add up."

Harper also said the Liberals want to get rid of the programs like income splitting for seniors and tax-free savings accounts, neither of which is true, Trudeau said after question period.

"I think it's obvious that the Conservatives are once again making things up to try and throw mud and see what sticks."

Since the Liberal plan was introduced last week, the Conservatives have criticized their rivals for announcing such a big-ticket promise without explaining how they would pay for part of it.

Employment Minister Pierre Poilievre has called the gap the "$2-billion hole."

The Liberals say their child benefit would cost the federal treasury $4 billion a year -- paid for, in part, by ditching the Conservatives' $2-billion income-splitting measure. As for the other $2 billion, the Liberals say they'll reveal the source of that money when they release their full campaign platform.

During a separate exchange during question period Tuesday, Poilievre took visible delight in pointing out that the Liberals had indeed made a subtle change in the way they are presenting their numbers.

In defending their position, the Liberals said the Conservative child care benefit would be worth $7 billion, taking into account the foregone government revenue. The combined cost of the existing child tax benefit and national child benefit supplement was pegged at $11 billion.

One of the charts in the printed Liberal material, however, showed the breakdown as $8 billion and $10 billion. A new, updated chart now only shows the combined cost of all those programs at $18 billion.

The Liberals called the change a design decision that simplified the chart, insisting the $18-billion calculation for the programs remained consistent.

Poilievre, however, begged to differ.

"They have actually changed the bar graph in that plan only one week after introducing it," he crowed, brandishing the relevant page of the Liberal document. "They are still billions of dollars short."