Clark, who inherited the carbon tax from Gordon Campbell, is now its de-facto spokesperson and will be the one having to rally her colleagues around the currently unpopular idea.
She can argue her province has had success with a $30 per tonne tax, without hindering economic growth.
"We have proven over eight long years of doing this, that having a carbon tax doesn't have to hurt the economy," said Clark. "We are the fastest growing economy in the country while we have had the highest, broadest carbon tax. Why? Because it has been totally revenue neutral."
Clark argues B.C.'s revenue-neutral model — where money collected is returned in the form of a reduction in other taxes — will work elsewhere.
"Every carbon tax in the country needs to be revenue neutral for individuals. I don't think you can build support for environmental protections that make people poorer," says Clark. "You can only build consensus around these type of changes if it makes people wealthier, which is what we have done in B.C."
On the surface, it sounds like a compelling pitch. But on a political level carbon taxes are still hugely unpopular.
Provinces that rely heavily on developing fossil fuels like Alberta and Saskatchewan ruled out a carbon tax even before the meetings got underway.
The country's two biggest provinces, Ontario and Quebec, have a cap and trade system that punishes companies for growing their carbon footprints.
But the provinces against the tax are now in the tough position of either deciding on some sort of carbon pricing themselves or having it forced on them the prime minister.
Trudeau did not go as far as saying he would impose the tax, but the understanding is that every province will have at least some model of carbon pricing, and that provinces risk losing the revenue the tax creates if they cede control to the federal government.