Coun. Tom Hamilton has even suggested the town consider taking over responsibility for the library.
"Maybe it's time we take the library on," Hamilton said at the Dec. 6 council meeting.
The issue came up when representatives of the Hay River Library Committee were asked to appear before council about its request for $114,000 in 2005.
The library is funded by both the town and the GNWT.
Coun. Ron Cook, while saying he doesn't agree with taking over the library, would like to see the funding issue sorted out.
"This thing has been beaten around the bush for a long time," Cook said.
The town's increasing financial support seems to be an example of territorial government downloading, he said.
Among his other concerns is the deterioration of the library grounds over the last few years, noting it used to be one of the best kept properties in town.
"Now it is deteriorated to one of the worst," he said.
Coun. Robert Bouchard would like to understand what the cost would be if the town took over the library.
Library committee treasurer Braam Burrub said neither the town nor the GNWT wants to take full responsibility for the library, which is officially known as the NWT Centennial Library.
"We're trying to look for some kind of certainty so we can continue to operate and provide services to the community," Burrub said.
"I guess we're a bit of a hot potato."
The town's contribution to the library has increased from about $56,000 six years ago.
The budget request from the library includes $8,000 for book collection development.
"Our library has an aging book collection that needs to be updated," Burrub said.