The increasing flow of hundreds of asylum-seekers of African and Middle Eastern origin from the United States in recent months is becoming a contentious issue in Canada.
Although there has been broad bipartisan support for high levels of legal immigration for decades in Canada, Trudeau is under pressure over the flow of the illegal migrants.
He is questioned about it almost every time he appears in parliament, from opponents on the left, who want more asylum-seekers to be allowed in, and critics on the right, who say the migrants pose a potential security risk.
Canadian opposition parties seized on the poll results, with both those on the left and the right saying they underscored their positions.
Canadians appeared to be just as concerned about illegal immigration as American, according to the poll, which was conducted between March 8-9. Some 48 per cent supported "increasing the deportation of people living in Canada illegally."
When asked specifically about the recent border crossings, the same number - 48 per cent - said Canada should "send these migrants back to the U.S." Another 36 per cent said Canada should "accept these migrants".
Illegal migrants interviewed by Reuters in Canada said they had been living legally in the United States and had applied for asylum there. But they fled for fear of being enmeshed in Trump's immigration crackdown.
Kevin O'Leary and Kellie Leitch, top contenders to be leader of the official opposition right-leaning Conservative Party, both said the poll showed they were right to demand Ottawa deter border crossers.
Like Trump, O'Leary is a brash businessman and television personality with little experience of politics.
The left-leaning opposition New Democrats said given the poll showed Canadians wanted asylum seekers to cross the border legally, Ottawa should suspend an agreement with the United States whereby Canada turns back refugees from the United States if they try to make claims at border crossings.