The country traditionally enjoys bipartisan support for high levels of legal immigration
The shock poll, by Reuters/Ipsos, found nearly half of Canadians want to deport illegal immigrants crossing into the country from America.
And a similar number – 46 per cent – were displeased with the prime minister’s efforts in handling the influx.
The country traditionally enjoys bipartisan support for high levels of legal immigration into Canada, but Mr Trudeau has come under criticism for steady flow of illegal migrants.
Some 41 per cent of adults asked in the poll said they thought the high numbers of illegal immigrants would make Canada less safe.
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The controversial issue could present a major risk to Mr Trudeau’s Liberal government, as he faces grilling from the left and right over the situation.
Brian Lee Crowley, head of the Macdonald-Laurier Institute public policy think-tank, said: “If people become convinced there's a large uncontrolled flow of illegal immigrants, I think that will be a very serious political issue for the government.”
The poll, conducted earlier this month, has revealed Canadians are nearly as disapproving of illegal immigrants as Americans.
The controversial issue could present a major risk to Mr Trudeau’s Liberal government
Some 48 per cent said they supported "increasing the deportation of people living in Canada illegally".
And when asked specifically about border crossings, the same amount thought Canada should "send these migrants back to the US”.
In contrast, 36 per cent said the county should “accept these migrants”.
Refugees are much more welcomed when we have gone and selected them ourselves
In the US, another Reuter/Ipsos poll found 50 per cent of Americans supported "increasing the deportation of illegal immigrants”.
Some illegal migrants currently living in Canada said they had fled the US for fear of being deported under Mr Trump’s tough new crackdown on immigration.
Greg Janzen, elected leader of a Manitoba border municipality, said: “There are so many people in the world who want to come in and go through the right channels.
46 per cent were displeased with the prime minister’s efforts
"That's what's p***ing most people off. These guys are jumping the border.”
And Janet Dench, executive director of Canadian Council for Refugees, said: "Refugees are much more welcomed when we have gone and selected them ourselves as a country, as opposed to refugees who have chosen us.”
The issue of immigration is one of Canada’s top priorities, ranking behind healthcare, taxes, unemployment and poverty.
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For this year, Ottawa set an immigration target of 300,000, or just under one per cent of the population, the same level as 2016.
But it reduced the 2017 target for resettled refugees to 25,000 from 44,800 in 2016.
The poll was conducted online in English and French throughout Canada.
It included responses from 1,001 people 18 years or older.
48 per cent thought Canada should "send these migrants back to the US
Individual responses were weighted according to the latest population estimates, so that the results reflect the entire population.
The recent poll also revealed the demographic of voters who supported a tougher stance on immigration.
Support was strongest for deportation among men, adults with no university degree, older people and those with higher levels of income.