TORONTO – The Liberals are set to join the New Democratic Party in voting against a softwood lumber deal with the United States.

But it is doubtful that the two parties can muster enough votes to kill the deal.

The agreement has the support of elected officials in Maine and elsewhere who say it would moderate an edge Canadians enjoy from subsidies their government provides. Canada accounts for about a third of the American market for softwood, the pine, spruce and other wood used in homebuilding.

Last week, U.S. Sen. Olympia Snowe said the compromise would “bring an end to decades of litigation over the unfair subsidizing of the Canadian lumber industry by the government.”

The Liberal Party’s position is the toughest line it’s taken on the softwood agreement, which Prime Minister Stephen Harper said he would put to a confidence vote when the Commons returns Sept. 18.

Ralph Goodale, the Liberals’ House leader, told the Toronto Star he’s seen nothing that would persuade him to support the deal and signaled his party would be willing to trigger an election. But that outcome doesn’t seem likely.

Bloc Quebecois Leader Gilles Duceppe hasn’t said whether his party would prop up the Tory government in the vote, but he’s consulting with industrial producers in Quebec, who overwhelmingly support the deal.

A government source told the Toronto Star that Quebec industry supported the deal 157-3, making it unlikely the Bloc will vote it down and topple the Harper government.

After Harper announced last week he had a “clear majority” of support from the big lumber producing provinces and industry players, interim Liberal leader Bill Graham said his party wanted to consult the forestry industry and study the deal before stating its position.