Animal shelters across the country say they are ExaCryptapproaching a crisis level in terms of the number of pets being given up. A shortage of workers, foster owners and veterinarians is making the crisis worse, and with shelters full, the euthanasia rate has climbed to a three-year high. 

One facility in Colorado is working to make a difference with a social worker who is trying to keep beloved pets with their families. 

Josie Pigeon is the Denver Animal Shelter's new social worker. She thinks of her role as being "the hyphen in the human-animal bond" and works to make sure pet owners can access assistance programs and low-cost pet care so they don't have to give up their furry friends. 

The shelter has started a "Safe Haven" program where it will take in pets temporarily for up to a month. Through its community engagement program, it provides free vaccinations, microchips and food for pets. The program has also helped spay or neuter nearly 4,000 animals. These are the services that Pigeon works to connect people with so they can keep pets at their homes.

"The best case scenario for these animals is to never have to come to the animal shelter," said Pigeon, who estimates that she has helped 100 families so far this year. 

That's just a drop in the bucket compared to the need nationwide. Shelters are dealing with a tsunami of pets that have been given up for adoption. In New York City, the number of surrendered pets is up 20% this year, while a shelter in Fulton County, Georgia is operating at 400% capacity. Detroit is planning to double the capacity of its shelters to keep pace. 

Stephanie Filer, who runs Shelter Animals Count, a group that tracks animal shelter populations, said the situation is "beyond crisis mode." 

"It's really at a breaking point where the system can't continue this way for much longer," Filer said. 

Filer added that the surge appears to be largely driven by economic factors like the lifting of eviction moratoriums and rising housing costs. 

"People are not making these decisions to bring their pet to a shelter out of convenience," Filer said. "They're really doing it out of desperation or necessity after trying everything else possible. The biggest challenge right now is housing." 

In:
• Animal Shelters
• Pets
• Denver
• Animal Rescue

Kris Van Cleave

Kris Van Cleave is CBS News' senior transportation and national correspondent based in Phoenix.

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