Nearly half of the workers in Duluth never get a paid sick day.

Debra Smith’s job at a temp agency supplied her with full-time work at up to $12 an hour, but no benefits. If she got sick, or if she needed to stay home to care for her daughter, who has asthma, it came out of her paycheck.

“I couldn’t take time off work — or felt that if I did, I would be paid less,” Smith said Monday at a news conference organized by Take Action Minnesota, a nonprofit focused on racial and economic equity. “That would affect my ability to pay the rent, or purchase groceries.”

Smith, who now works a job with better benefits, was one of nearly 20,000 Duluth workers who do not get paid sick leave. Roughly 46 percent of the city’s workforce has no paid leave, according to a new survey by the Institute for Women’s Policy Research.

Duluth is now joining a growing number of Minnesota cities looking to implement paid sick leave regulations for businesses. Minneapolis, where an estimated 42 percent of the workforce lacks paid sick leave, is working on a plan to require businesses with four or more employees to offer that benefit. St. Paul is studying the idea of mandatory sick leave benefits as well.

Researchers studied census and National Institutes of Health data to determine how many Duluth workers had access to paid time off when they were sick. In 2014, a statewide survey found that Duluth and St. Louis County had the lowest rate of sick leave coverage in Minnesota. The 2016 follow-up found that workers with the smallest paychecks were also the least likely to have access to benefits such as sick days.

Part-time workers and employees who earn less than $35,000 a year were least likely to have access to paid time off when they or a family member fall ill. By contrast, almost all employees in the top salary tiers, the ones earning more than $65,000 a year, had paid sick leave.

Four states — California, Connecticut, Massachusetts and Oregon — require employers to offer sick leave. Twenty-three cities have also instituted their own mandatory requirements.

But mandatory sick leave can be a tough sell, particularly to businesses. Duluth is a city of small businesses with big concerns about how they would handle the cost if the city imposed a sick leave policy.

“How much do you want to pay for a burger?” said Tony Boen, regional manager for Grandma’s Restaurant Co., a Duluth chain with 400 to 600 employees, depending on the time of year. Businesses, he said, might be forced to pass the cost of expanded benefits on to their customers, in the form of higher prices. And if customers balk at paying, businesses might have to start cutting jobs, he warned.

“Our employees are our number one resource. We’ll do everything we can to keep our employees healthy and happy and satisfied,” he said. “We can do that without an ordinance.”

Since no restaurant — and no city health department — wants food service workers showing up sick, Grandma’s allows employees to call in sick, then works with them to help them make up the missed hours once they’re well. But Boen said there is room for the city and its businesses to sit down and discuss ideas for improving workplace sick leave policies.

A bill that would have extended sick pay and family leave to 136,000 Minnesota workers — an estimated $461.8 million in benefits each year — foundered in the Legislature. Businesses worry about one-size-fits-all policies being applied to workplaces that range from mom-and-pop storefronts to construction sites to white-collar offices.

Take Action and the other advocate groups are still working out the details of the paid leave policy they would like to see Duluth implement.

In a statement Monday, Duluth Mayor Emily Larson said she is committed to extending sick time and family leave to all city government employees and to starting a conversation about the issue in the wider community.