Undocumented immigrants in the United States are fleeing to Canada. But Canadians may not want them, a new survey finds.

Nearly half of Canadians support "increasing the deportation of people living in Canada illegally," according to a Reuters/Ipsos poll released Monday. The same share said they supported sending migrants that crossed from the United States right back over the border, while just 36 percent said Canada should accept them and let them apply for refugee status.

The popular sentiment could pose a challenge to Canadian Prime Minister Justin Trudeau, who champions a pro-refugee and pro-immigration policy as a stark foil to U.S. President Donald Trump.

Trump's anti-immigrant "build a wall" rhetoric launched him into the White House, but since getting there, he has faced significant political backlash and legal scrutiny over his policies. The debate is spilling over into Canada, where Trudeau is taking a political hit for keeping his country's door open to refugees and immigrants. Forty-six percent of poll respondents disagreed with how Trudeau is handling the immigration situation, compared to 37 percent who agreed.

While Canadians are split on Trudeau's policies, the poll clearly shows the national debate over immigration is heating up. Nearly a quarter of Canadians believe immigration control to be a leading national issue, compared to 19 percent in a December poll. And some 40 percent thought accepting those fleeing from the United States could make Canada less safe.

Undocumented immigrants began fleeing to Canada in record numbers amid Trump's political rise. In 2016, 1,222 fled the United States to Quebec alone, a fivefold increase from years past. Those who fled in January and February, after Trump first stepped into the Oval Office, risked frostbite and hypothermia to cross to Canada.

Canadian rights groups pin the blame solely on Donald Trump and his heavy-handed executive orders to crackdown on immigration. "There's no question what's driving them," Paul Caulford, a doctor at the Canadian Centre for Refugee and Immigrant Healthcare outside Toronto, told Public Radio International in February. "Virtually every person who's crossed, from pregnant women in the back of trucks to those shepherding their children to safety, have said to us that the United States is no longer a safe country for them to be in."

While the debate heats up, Canadian authorities insist they are upholding strict immigration standards at the border. Canadian authorities detain all asylum-seekers they find who slip across the border to escape Trump's net. "If they are found to be inadmissible without a valid claim, deportation procedures are begun," Dan Brien, a spokesman for Canadian Public Safety Minister Ralph Goodale, told Reuters.

Trudeau's Liberal Party won't face elections again until 2019. But experts say border crossings could surge when the weather warms up and Canada's southern neighbor piles tightens the bolts on its immigration crackdown.