The promise of "sunny ways" was not, as it turns out, a commitment to agree with whatever any or every provincial government demanded.

That much became abruptly apparent two weeks ago when the prime minister stood up in the House of Commons and announced that there would be a national price on carbon applied in each province, whether or not every premier agreed to do so.

And now, while the grumbling over carbon is still being heard, a multi-billion-dollar difference of opinion looms as the provincial and territorial ministers of health prepare to meet with the federal minister in Toronto on Tuesday.

On Monday, provincial health ministers and finance ministers will meet amongst themselves in Toronto.

Officially, Tuesday's discussion is expected to cover a number of issues — Indigenous health, pharmaceuticals, opioids — but it is the subject of federal-provincial health accords and, more specifically, the precise amount of funding the federal government should be transferring to provincial governments for health care that might overshadow all else.

And, according to briefing notes for Health Minister Jane Philpott obtained by the CBC, the federal government is coming to this week's meeting armed with numbers to question the case provincial governments are making for a six-per-cent annual increase in health care funding.

How we got here

The basis for this debate dates to 2004, when Paul Martin committed to a 10-year deal with the provinces on funding for health care. With that deal, the annual federal health transfer was scheduled to increase by six per cent each year.

Seven years later, when it came time to discuss a new funding agreement, Stephen Harper's government decided that, starting with the 2016-17 fiscal year, annual funding would increase at the rate of growth in Canada's nominal GDP, with a commitment to at least an additional three-per-cent each year.

This much was simply declared by Jim Flaherty, the finance minister of the day. Several of the provincial governments were rather unimpressed.

Philpott is now offering $3 billion more over four years, but with a demand that the money be directed to home care and palliative care. Beyond that, the Liberal government is not offering an increase in the annual escalator.

And so the disagreement has been renewed.

The federal argument for a smaller increase in base funding

The federal minister has nodded at the government's line of argument already.

"While investments in the transfer have increased at a rate of six per cent per year for the last decade, provincial health spending has not increased at that rate," she told the House of Commons earlier this month in response to an NDP demand that the escalator be reset to six. "It has been less than two per cent."

The federal background document, citing data from the Canadian Institute for Health Information, notes that provinces increased spending each year on health care by an average rate of 2.6 per cent over the last five fiscal years. (Over the 10 years previous to that, the average annual increase was seven per cent.)

"In Quebec, we went through a huge reform where we saved money, we controlled the budget increases year-over-year at two per cent for the past three budgets," Quebec Health Minister Gaetan Barrette said last month in an interview with CBC's Power & Politics. "We did our part, we did the right thing, but even then there are areas in health care that we have difficulty to provide care for, like home care and like mental illnesses."

Philpott has also focused on mental health as an area of concern.

Provincial governments counter with a different figure, arguing that the federal government should cover 25 per cent of the total cost to governments of health care in Canada.

The Trudeau government says the federal share has increased in recent years, but, according to their data, for 2015-16 it will sit at 23.5 per cent, still short of the provincial goal.

Of course, the federal share depends somewhat on the total cost.

How much should governments be spending on health care?

In 2012, the parliamentary budget officer projected that, if Flaherty's formula was maintained indefinitely, the federal share of health spending would gradually decline. But that analysis projected that spending by the provinces would increase by slightly more than five per cent annually.

An aging population could be expected to increase public costs in the years ahead, but, in a recent speech, Philpott argued that investing in home care could reduce those expenses.

Philpott also identified reducing drug costs as a potential source of savings and argued for a focus on innovation within the health system, both with the involvement of the federal government.

But, last month, Barrette argued that to reach 25 per cent, a six-per-cent escalator would have to be maintained for another decade.

Another provincial concern is that any additional funding by the federal government be provided long-term, lest provinces be left with the entire cost of maintaining new programs.

All of which might open a discussion about the cost and performance of the Canadian health-care system.

"As we have said all along, we are committed to working collaboratively with provinces, territories and indigenous partners on ways to promote shared priorities," says Kate Purchase, the prime minister's director of communications. "But first, Canadians must be assured that new investments made by the federal government will be used for health-care. That has to be the basis for any further conversation."

Just how difficult a conversation that will be, whether it will include significant new sums of federal funding and, if so, in what form, remains to be seen.