The 46-year-old has answered rising discontent in Canada over the sluggish economy and the acceptance of 37,000 Syrian refugees.
Fresh polls show Leitch is ahead of about a dozen candidates in the Conservative leadership election scheduled to be held on May 27, 2017.
The candidate chosen by party members will be their flag bearer for the October 2019 general election, against Prime Minister Justin Trudeau’s Liberals.
In an interview last week from her farmhouse in rural Ontario, Leitch said: “Elites pretend this isn’t an issue, but Canadians want to talk about it (immigration).
“I am talking about screening immigrants, I am talking about building pipelines, I am talking about making sure Canadians have jobs, so yeah, some of the ideas and language are the same.”
One of the reasons why the Conservatives had managed to hold power for almost a decade was their successful push into immigrant communities under former Prime Minister Stephen Harper, who had convinced the party that rising immigration made newcomers a must-win constituency.
Canada takes in about 300,000 immigrants every year.
A November poll by Mainstreet/Postmedia showed Leitch led a 12-candidate Conservative race with 19 percent support, and separate data showed she led fundraising as well.
The pool of candidates running has since swelled to 14, and more may join, including businessman and reality TV star Kevin O’Leary, who has also drawn comparisons to Trump.
He said: ”The type of forces driving Brexit and Trump are very much at work in Canada, albeit somewhat more muted.”
Canadians have drawn parallels between her “Canadian values” and Trump’s “Make America great again” campaign.
A practicing Catholic from the traditionally conservative, oil-rich province of Alberta, Leitch, said she has no fear of the media backlash.
Trudeau was elected in October 2015 and promised to accept more Syrian refugees more quickly than the Conservatives, who had been in power for nearly 10 years.