Officials from emissary provinces New Brunswick, Prince Edward Island and British Columbia will meet with Kenney in Toronto after all the provinces and territories agreed to the terms of the counter-proposal last week.
They're united on measures that would give them more leeway in how they fund the program. The provincial proposals would also make it less financially onerous for small businesses to participate in the Canada Job Grant.
But an official close to the talks says the provinces are seeking flexibility in funding that goes well beyond what Kenney offered them in a revised Job Grant proposal in late December. The Canada Job Grant is slated to take effect on April 1.
Under the original proposal, the government would have issued $15,000 grants to eligible Canadians, with the cost divided three ways between Ottawa, the provinces and interested employers. The goal of the program is to compel employers to train their future and current workers, and to encourage provinces to focus on training that will result in actual employment.
Ottawa currently provides the provinces with $500 million a year in funding under existing labour market agreements that expire on March 31. Under the Job Grant, the provinces would have lost $300 million of those funds, or nearly 60 per cent.
Amid vehement opposition from the provinces and territories about the $300 million hit, the government then revised its original proposal by offering to cover the provincial share, bringing its own contribution up to $10,000 per grant.
Kenney said he accepted that the provinces didn't have the ability to match Ottawa's funding, and was intent on seeking common ground.
Nick Koolsbergen, a spokesman for Kenney, said Monday that the minister is looking forward to the meeting with provincial officials.
"The federal government has listened to provinces' concerns and significantly restructured the offer based on their feedback," he said in an email.
Brad Duguid, Ontario's minister of training, colleges and universities, suggested last week that there remains daylight between the provinces and the federal government when it comes to the Job Grant program.
He said Kenney's revised offer would still divert $300 million from existing programs aimed at helping aboriginals, immigrants, women, youth, older workers, people with disabilities and those with low literacy levels — a move he said has left him "perplexed" because of the success rate of those programs.
Another trouble spot is the fact that the provinces would be on the hook for any funding shortfalls that could result from a lack of business participation in the program. Duguid said the provinces shouldn't have to bear the financial responsibility for a national program that's untested and untried.
But other stakeholders have complained that under Kenney's revised offer, the number of grants will be reduced — lessening the impact of the program — because the federal government isn't offering up any new money.
Indeed, several labour unions and trade associations preferred the Job Grant in its original form, before revisions. Its boosters included the Canada Building Trades Union, the Progressive Contractors Association of Canada and the National Association of Career Colleges.
"The Canada Job Grant is an attempt to realign priorities, to nudge provincial and other partners, to effectively improve training delivery in Canada," said Robert Blakely, director of Canadian affairs for the U.S. labour federation AFL-CIO.
"This is the kind of action Canadians should expect from government at all levels."
Follow Lee-Anne Goodman on Twitter at @leeanne25
Also on HuffPost