In the first two months of 2017 around 1,700 refugee claims were filed at the Canadian-US border, according to the Canada Border Services Agency.
Forty-six per cent said illegal immigration makes no difference to Canada's safety, while 41 per cent felt it would make the country less safe.
As refugees continue flocking to Canada, a new Reuters/Ipsos poll found nearly half of Canadians want to deport those who illegally cross into the country.
In response to Trump's travel ban, Canadian Prime Minister Justin Trudeau announced in late January that "those fleeing persecution, terror & war" are welcome in Canada.
Of those polled, 46 percent disagreed with how the prime minister was handling the border crossings.
The Canadian government set an immigration target of 300,000 for 2017, or just under 1 percent of the population, the same level as 2016.
The same number of respondents suggested that the migrants should be sent back to the United States, while 36 percent said Canada should "accept these migrants" and allow them to apply for asylum.
In the United States, where President Donald Trump was elected partly on his promise to boost deportations, 50 percent of adults supported "increasing the deportation of illegal immigrants", according to a separate Reuters/Ipsos poll that was conducted during the same week in the United States.
CBC News reported last week that more than 200 asylum seekers from around the world have walked north across the Canadian province of Manitoba's shared border with North Dakota and Minnesota and into the town of Emerson, Manitoba, since the beginning of the year.
After reaching Canada, many people illegally crossing the border wind up at the Manitoba Interfaith Immigration Council, which provides legal assistance for refugees looking for asylum.
That also occurs, in part, because those in the U.S. can't apply for asylum in Canada, as the U.S. is considered safe country.
"That's what's pissing most people off".
The PMO is not commenting on the poll, however, a spokesperson for the Public Safety Minister says slipping across the border is not a "free ticket" into Canada.
Warm weather may lead to an even greater spike in illegal immigration into Canada, warned Brian Lee Crowley, head of the Macdonald-Laurier Institute public think-tank. 37% said they agreed with government's current immigration policy.
But Canadians are becoming increasingly concerned about those who don't follow the proper legal channels to enter the country.
"If they are found to be inadmissible without a valid claim, deportation procedures are begun", he said, adding that those who are believed to pose a risk can be detained.