A 37-day strike at five Allina Health hospitals ended Tuesday night, but nurses left the picket lines with concerns about the contract they must approve before returning to work.

In huddles during the final day of picketing and on social media, nurses debated the offer their negotiators reached during a 17-hour bargaining session arranged by Gov. Mark Dayton at his official residence.

“Sounds like a cave. Don’t do it,” said nurse Deanna Pulver on the Minnesota Nurses Association Facebook page. “What was the purpose of the past 6 weeks then?”

Since May, the nurses have rejected three contracts over Allina’s demand to replace their low-deductible union health plans with Allina’s corporate plans. The first no vote resulted in a one-week strike in June and the second prompted the open-ended strike that started on Labor Day.

But around 4:30 a.m. Tuesday, union leaders emerged from the governor’s residence with the first proposal they could recommend to the rank-and-file. While it still phases out the union health plans by 2019, it guarantees that the benefits of Allina’s most popular plan would remain unchanged through 2021.

“We started with nothing in the beginning of this whole negotiating process,” said Angela Becchetti, a nurse at Abbott Northwestern Hospital and a member of the union negotiating team, “and now we’re [promised stable benefits] through the end of 2021.”

Prior proposals offered the nurses $500 cash bonuses, she added, but the latest proposal offered up to $2,500 in tax-favored payments to nurses’ health reimbursement or health savings accounts over the next five years.

Voting is scheduled Thursday for more than 4,000 nurses from five Allina hospitals: United in St. Paul, Mercy in Coon Rapids, Unity in Fridley, and Abbott and the Phillips Eye Institute in Minneapolis.

Allina officials declined to comment beyond a letter from the health system’s chief executive, Dr. Penny Wheeler, who called the offer “fair to our nurses and sustainable for our organization.”

“This has been an emotional time for all of us, and I know that strong feelings won’t vanish overnight,” Wheeler wrote. “But I also know that every one of us — nurses and non-nurses alike — share a deep and abiding commitment to providing exceptional care to the communities we serve. That common thread will be what will pull us back together.”

Whether criticism by individual nurses will affect overall voting is unclear. After a one-day strike by 12,000 nurses from multiple ­hospital systems in 2010, some criticized a contract offer that lacked their demand for fixed staffing ratios. But nurses still approved the agreement.

In the latest proposal, Allina agreed to 24-hour security staffing in its emergency departments — a key issue for nurses in an era of increasing hospital violence. Also, a joint committee would address staffing issues, such as charge nurses with patients of their own — having too little time to properly supervise and support front-line nurses.

Dawn Yetter, a nurse at Unity for 37 years, said nurses deserve more than what is provided in Allina’s latest offer. But she said but voting no and resuming the strike would likely cause them more ­financial pain.

Between the two strikes this year, nurses have been off work for 44 days — exceeding the 38-day walkout in 1984 that was the longest nurse strike in state history.

“A lot of nurses are hurting out on strike,” Yetter said.

‘Important for patients’

Dayton and Lt. Gov. Tina Smith invited the two sides to the governor’s official residence after nurses voted down a contract offer on Oct. 3. The governor encouraged them to reach a deal before they left.

The unusual bargaining session also marked the first time that Wheeler attended negotiations, something nurses had sought for months.

At some points, Allina and union officials met face to face — something that hadn’t happened in prior mediated sessions. At other points, a federal mediator and Smith acted as go-betweens.

“Both the governor and I were clear that we thought an agreement could be reached — that it was important for the hospitals and the nurses and especially the patients,” Smith said in an interview Tuesday afternoon

Becchetti commended Dayton and Smith for kick-starting talks by getting Wheeler to attend: “I just did not see the Allina Health negotiating team as it was structured getting a deal done that worked for both parties.”

The strike has taken a toll on both sides.

While Allina anticipates saving $10 million per year by phasing out the union health plans, it spent $20 million on temporary staffing to keep operating during the one-week strike in June. The costs of the current strike have far exceeded that.

The union reported last week that 200 nurses have left Allina since June, while Allina countered that more than 630 nurses have crossed the picket line and returned to work.

Yetter worked at the Ryder Cup and donated plasma for extra income during the strike, but her husband’s work kept her family afloat. She worried more about younger nurses, many of whom didn’t need the rich benefits of the union health plans but stayed out on strike.

“They’re out there picketing and losing money for something that doesn’t even really affect them,” she said. “There comes a point when you have to decide what’s fair for everyone.”