Relations between Stop & Shop and its New England unions have "gone from bad to worse," according to a spokeswoman for the workers, and both sides say no further bargaining sessions are scheduled.

One union head is even suggesting a strike may be inevitable.

"I just don't think they're going to have enough on the table, when we get to the end of the road," Jeff Bollen, president of United Food and Commercial Workers Local 1445, said Thursday in a video message to members. "I really believe that they're gonna try to still demand some kind of givebacks and concessions and, with that, we will be going out."

Bollen represents about one-third of the 31,000 New England workers who have authorized a strike but have not yet called one. Amy Ritter, a spokeswoman for the five UFCW unions negotiating with Stop & Shop, said there is no immediate plan to strike and that the labor group "remains willing to bargain with the company at this time."

Stop & Shop said in a statement that "although no additional dates have been scheduled, we remain available, as always, for more negotiation dates and hope to receive substantive and constructive union responses to our recent suggestions."

The company previously said it is planning for the possibility of a strike and would hire temporary workers to keep stores open.

Stop & Shop's contract with its New England unions expired Feb. 23.

Both sides have declined to discuss their offers in depth, but health care is one central issue. Bollen said in his video message that Stop & Shop's original proposal asked workers to quadruple their contributions to insurance premiums; the company now wants workers to double their payments, he said.

A Stop & Shop spokeswoman would not confirm or deny Bollen's figures but said, "Stop & Shop associates' deductibles and employee health plan contributions have remained far below national averages."

"The share of health-care premiums paid by Stop & Shop associates currently averages 8.2 percent of the cost of single coverage and 6.6 percent of the cost of family coverage," added the spokeswoman, Jennifer Brogan.

Brogan pointed to national averages in the Kaiser Family Foundation's 2018 Employer Health Benefit Survey, which showed workers typically pay 17 percent of the cost of single coverage and 28 percent of the cost of family coverage.