When Baloo, a big white rabbit, and his brother Elliott were surrendered to an animal shelter outside Montreal, Canada, the countdown started.

Strapped for money and overcrowded, the shelter put the word out to rescue organizations that the rabbits would be euthanized in three days unless someone stepped up to take them. The shelter had so many rabbits, according to Haviva Porter, who runs Rabbit Rescue Inc., a Toronto-based nonprofit, that it wasn’t even listing them for public adoption.

“This has been the worst year ever in 20 years of rescue,” Porter says.

Animal rescuers across the United States and Canada echo her experience. “It’s been a sea change the last few months,” says Joe Labiola, director of PAWS Atlanta animal shelter. He says the shelter is getting by—but only just.