Romanow told CBC News that the premiers are doing what they can, but they need the support of the federal government to cut costs and improve service.
Responsibility for health care is shared between the two levels of government, he said.
The premiers are trying to talk to Harper, but he won't meet with them, Romanow said. A meaningful dialogue is more important than increasing the current funding, he added.
Romanow, who also led a royal commission on the future of health care, spoke to CBC on Tuesday ahead of the premiers' annual meeting in Niagara-on-the-Lake, Ont.
New poll released
Health care remains an important issue for Canadians, a new poll suggests.
The poll was commissioned by a group urging more funding for public health care. The Canadian Health Coalition is backed by national unions, as well as church and anti-poverty groups.
The poll suggests 89 per cent of Canadians support or somewhat support "public solutions" to strengthen public health care.
More than half of those polled, 54 per cent, said they thought the health-care system would be weakened if private for-profit health-care services were expanded. Another 28 per cent said they thought private care could make the system stronger, with eight per cent saying they didn't know.
The poll, conducted by Nanos Research, is being released just ahead of the Council of the Federation, the annual meeting of Canada's premiers.
The survey of 1,000 Canadians was conducted between July 13 and 17, 2013. It was done online following a random recruitment by telephone. The results were statistically checked and weighted using the latest census data.
The margin of error is plus or minus 3.1 per cent, 19 times out of 20.
Health care on the agenda
Federal Finance Minister Jim Flaherty presented his provincial and territorial colleagues with a take-it-or-leave-it deal at the end of 2011, three years before their current funding arrangement was supposed to expire.
Flaherty told the provincial and territorial finance ministers that the federal government would keep increasing health-care funding by six per cent a year until the 2016-17 fiscal year.
But starting in 2016, the amount given to the provinces will be tied to economic growth. The government will link the amount to nominal GDP, the monetary value of all goods and services produced within the country annually, including inflation. If nominal GDP rises four per cent and inflation is two per cent, the economy's real GDP growth is two per cent.
Flaherty said the provinces and territories will get at least three per cent increases.
Since then, Canada's premiers have been working on ways to cut costs from the health-care system.
A subcommittee led by Prince Edward Island Premier Robert Ghiz and Saskatchewan Premier Brad Wall have already reported on buying generic drugs in bulk and how to smooth hospital operations to save time and money.
This week, they'll discuss long-term care versus homecare for seniors, as well as when diagnostics are required, and how to lower the prices of brand-name drugs for the provinces.
Romanow says the amount of money pledged to the provinces and territories is less of a concern than getting the federal government working with them.
But the premiers are spending most of their time on other issues, including bullying, a national energy strategy, and jobs and training.
The poll suggests half of Canadians, or 51 per cent, want the prime minister to call a meeting about health care with the premiers. The poll says another 29 per cent would somewhat support that call. Respondents weren't asked what such a meeting would achieve or what specifically would be discussed.
The poll also suggests 22 per cent of respondents would be very likely to switch allegiance to another political party if the party they currently support "failed to present a plan for the future of health care."
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