Federal cabinet ministers are set for an in-depth discussion this week of the practical and political pressures being placed on the Liberal government by a rising number of asylum seekers in Canada.

Border security, RCMP and immigration officials have been running scenarios to prepare for the possibility that a relative winter trickle of illegal immigration into Canada could turn into a spring flood.

The results of their table-top exercises will help form options being put before cabinet Tuesday, The Canadian Press has learned.

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Officials are also studying links between distinct groups of border-crossers that might belie the common notion they're all being pushed into Canada by the volatile U.S. political climate.

Two government officials confirmed to The Canadian Press that many of the people coming into Quebec hold American visas issued at the U.S. Embassy in Riyadh, Saudi Arabia.

Interviews revealed the visas were obtained to use the U.S. as a transit point get to Canada and claim asylum — plans set in motion long before the U.S. election in November, the officials said, neither of whom were authorized to publicly discuss the issue.

But it is the pictures of RCMP officers hoisting small children above snow-covered fields along the Canada-U.S. frontier that have drawn global attention and placed political pressure on the Trudeau government from all sides.

The Opposition Conservatives are demanding a crackdown, and want those crossing illegally charged with crimes, something the government notes cannot happen until asylum claims are heard.

The fact those claims are being fed into a clogged system has others urging the Liberals to put more resources into the refugee-determination process and the agencies that support newcomers.

"We are the endpoint," said Chris Friesen, director of settlement services for the Immigrant Services Society of British Columbia.

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The Immigration and Refugee Board reported in its last quarterly financial document that in the first nine months of 2016-17, there was a 40-per-cent increase in new claims compared to the same period the previous year.

Statistics provided to The Canadian Press show claim levels generally began rising in Canada before U.S. President Donald Trump took office.

In fact, the increase seems to have begun just as Prime Minister Justin Trudeau took power.

In October 2015, the month of the last federal election, 1,519 claims were lodged in Canada. The next month, when the Trudeau Liberals took office, there were 1,647 and — with the exception of two months in 2016 — they have been rising since.

Trump is pushing people into Canada, but the Trudeau government's repeated messaging on welcoming diversity and immigration is a pretty strong pull factor, Friesen said. "We are now the beacon of hope for desperate refugees."

In B.C., there has been a 60-per-cent increase in the number of refugee claimants in the last 12 months compared to the previous one-year period. Most are Iraqi Kurds and Afghans, and there were also 18 undocumented Latin Americans from Guatemala, Honduras and Venezuela who recently crossed the Canada-U.S. border, immigration agencies said.

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The number of Mexican claimants is also starting to rise in B.C., following the end of a requirement for Mexican citizens to have a visa to enter Canada. During the last three months, there were 29 refugee claimants from Mexico, the agencies reported, compared to 30 who arrived between December 2015 and November 2016.

The Immigration and Refugee board is already adjusting to deal with the bigger numbers, but cabinet will consider giving it more resources.

Ministers will also consider whether there is room to alter the Safe Third Country Agreement between Canada and the U.S. The agreement says a refugee claimant must apply for asylum in whichever of the two countries they arrive first — unless they qualify for an exception.

It is being singled out as the reason people are avoiding official border stations and crossing into Canada illegally, and there are calls for Ottawa to suspend the agreement.

Cabinet's decision could depend on the next iteration of Trump's executive order laying out a temporary ban on immigration from seven predominantly Muslim countries. The current order has been challenged by the courts and Trump is expected to release a revised version soon.

Not much can be done to stop the border-crossers, said Ward Elcock, who advised the former Conservative government on illegal migration after years running Canada's spy agency.

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Canada must keep talking to the Americans to find the source of the problem, but the reality is the numbers crossing into Canada remain a fraction of what countries in Europe are seeing, he said.

Still, no matter how many enter illegally, some voices will try to make it a political issue.

"It is seen as, you didn't control the flow of people into the country," Elcock said.