Their applications were shipped from Buffalo to Ottawa last year after the government closed the office in the U.S. city.
Applicants say the move has placed their efforts to apply for permanent residency in limbo, with processing times far exceeding what they had been led to believe initially.
About 10,000 applications seem to be stuck, said a spokeswoman for the group, which calls itself "the forgotten of Buffalo."
Some people have given up and left the country, while others are scrounging to get by in Canada, where they are so far unable to work or obtain health care as their temporary visas have expired, Michele Doiron told a news conference Tuesday on Parliament Hill.
"Depression, family separation, divorce, anxiety over the unknown — the forgotten of Buffalo have 10,000 personal stories," Doiron said.
The Buffalo office was closed last May as part of what Citizenship and Immigration Canada calls a reorganization of its processing network.
"Most of the files that were transferred from Buffalo to the Ottawa processing office will be completed by summer 2013," said department spokeswoman Nancy Caron.
"New applicants are also enjoying the benefit of faster processing times."
The closure of the office also represented a policy change.
When the office was open, students and temporary foreign workers whose visa had expired and who wanted to travel outside of Canada had to apply for a new visa in another country if they wanted to return.
Now, they can apply for that visa while in Canada.
The Opposition New Democrats have been pressing Immigration Minister Jason Kenney on the files for months.
"These immigrants deserve clear and transparent information from the government on the status of their applications," said NDP immigration critic Jinny Sims.
"Their applications must be made a priority and the government must provide additional resources so these people can finally obtain their permanent resident status. The government must deal with this serious blunder."
Countered Kenney spokeswoman Alexis Pavlich: "The office and work in Buffalo have been moved to Canada, creating jobs for Canadians. The NDP can explain why they are against jobs for Canadians."
The Liberals called the backlog an example of a department in budget-cut chaos — even as the minister talks about a planned overhaul of the immigration system.
"When will the minister stop focusing on rhetoric and start improving immigration services?," said Liberal MP Kevin Lamoureux.
Kenney said the government has moved to eliminate a pre-existing backlog of permanent residency applications, slicing it by half since taking office since 2006.
Several visa offices around the world have closed since last year's cost-cutting federal budget was unveiled. The most recent is the office in Seoul, which was announced on Tuesday. Visa files there will be shifted to Manila.Suggest a correction