Brad Wall, a vocal opponent of the upper house, made his case before the Council of the Federation meeting wrapped up, but there was no further discussion on the matter.
"Different premiers are at different spots in respect to their view on the Senate," he said during a break in the meeting.
There are more pressing issues, including the economy and health care, Wall said. "Frankly, disasters are happening that are far more important."
Ontario Premier Kathleen Wynne, who hosted the event, isn't in favour of abolishing the Senate, unlike her predecessor Dalton McGuinty.
It's something the federal government is dealing with, she said. Prime Minister Stephen Harper has referred it to the courts as a constitutional matter, she said.
There is "consternation and concern" about the behaviour of some senators, Wynne said, but that's a separate issue from the broader debate about the existence of the Senate.
"That's a different discussion and I don't think should be driven by a particular individual's behaviour," she added.
But P.E.I. Premier Robert Ghiz said he doesn't believe the premiers will be consulted about it when the time comes.
"Harper is not interested in even talking to the premiers about anything, so most likely he's not going to bring us together to talk about the Constitution or the Senate."
Ghiz said he's willing to try for an elected senate. But it isn't a priority for the premiers, he said, it's a "hot button issue."
British Columbia Premier Christy Clark refused to comment on her position on the upper chamber, dismissing it as a "huge distraction" from focusing on what matters — growing their economies.
Alberta Premier Alison Redford agreed, but added that she's in favour of an elected Senate.
Wall found an ally in Nova Scotia Premier Darrell Dexter, who pointed out that his province abolished its Senate in 1928.
"Through five elections, no one's ever asked me to reinstate it," he said.
That wasn't the only Senate joke. According to a high-ranking provincial official, one of the premiers quipped during the meeting: "We shouldn't abolish the Senate, we should abolish Mike Duffy."
Duffy, who represents P.E.I., is being investigated by the RCMP over his improperly claimed Senate expenses and for accepting a $90,000 cheque from Harper's former top aide. It's alleged that he misrepresented his primary residence as P.E.I. instead of Ottawa to collect thousands of dollars in false living and housing expenses.
The Mounties are also investigating the involvement of Nigel Wright, Harper's former chief of staff, in giving Duffy the money so he could reimburse the Senate for the expenses.
Wright resigned after admitting he gave the money to Duffy. Harper has insisted Wright did not tell him about the "gift" until after news of it leaked out.
Duffy isn't the only senator who's landed in hot water. More revelations about former Liberal Senator Mac Harb hit the front pages Friday, with the RCMP alleging he claimed an "uninhabitable" home as his primary residence in what they say was a plan to bilk taxpayers out of tens of thousands of dollars in expenses.
When Ghiz was asked about his position on the Senate, given that Duffy represents his province, Ghiz joked: "I thought he was an Ontario senator."
As Canada approaches its 150th anniversary, it should examine whether the Senate is fulfilling its purpose to represent the country's different regions, he said.
"Is that happening today? Some people would say no," Ghiz said. "So does it have to evolve so it can represent our regions across the country? I think it should."
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