Low-wage workers in so-called quick service restaurants like coffee and sandwich shops would be further strapped financially under a House-approved bill that would allow certain managers to share in pooled tips, according to a Bay State union leader who is urging the Senate to reject legislation also opposed by Attorney General Martha Coakley.

The House last week approved legislation sponsored by Rep. Linda Dorcena Forry (D-Dorchester) allowing some shift supervisors at quick-service restaurants like Dunkin Donuts to share in pooled tips as long as their managerial duties were limited to on-the-job training for wait staff and assigning employees to their posts.

Supporters argue that at many of these restaurants shift supervisors work alongside rank-and file employees serving customers and doing similar jobs for only a slightly higher wage despite their job title.

The bill, which has won strong the support in the past from the Dunkin Donuts Independent Franchise Owners, nearly became law last year but died on the session’s last day when state Sen. Steven Tolman (D-Brighton) objected to its consideration.

“If passed, this bill would cut into the already low wage earnings of the non-unionized Massachusetts service sector employees. As you know, these employees are amongst the most vulnerable of our workforce in Massachusetts. These workers typically need to work two to three jobs to provide for their families,” wrote Janice Loux, the executive vice president of Unite Here, in a letter to Senate President Therese Murray dated July 21.

The local chapter of Unite Here represents more than 6,300 hotel and food service workers in metro Boston.

Assistant Attorney General Jed Nosal, chief of Coakley’s business and labor bureau, also wrote to Sen. Frederick Berry, a Peabody Democrat and chair of the Senate Committee on Ethics and Rules, to express Coakley’s opposition to the bill that he said would “eliminate an important protection for low-wage service workers.”

“This bill will undermine the well-established principle that managers must be paid [by] their employer – not by wait staff tips, i.e. the hard-earned wages of those they supervise,” Nosal wrote in a letter last Thursday.

The bill (H2294) sponsored by Forry, co-chair of the Legislature’s Committee on Community Development and Small Business, would qualify shift supervisors to receive tips if their only managerial responsibilities included on-the-job training for wait staff and assigning employees to their posts.

The legislation is identical to the bill that cleared the House and Senate last year, but was returned by Gov. Deval Patrick with an amendment and died in the Senate after the House consented to the governor’s change.

Defining quick service restaurants as an establishment selling food or beverages where products are served to patrons primarily over the counter or at a drive-up window, Forry, in a statement to the News Service, said the bill intends to protect the ability of low-wage workers to collect tips by more clearly differentiating between managers and workers and discouraging litigation that has led to tips being refused to avoid dispute.

“This bill protects low-wage service workers in quick-service restaurants. Bottom line, tip jars are being removed from these establishments, which reduces the earnings for all service employees. The intent of this bill is to provide clarity that will discourage litigations, draw distinctions between managers and low-wage service workers, and allow these workers to supplement their incomes with tips,” Forry said.

Loux, however, said the change would cut into the earnings of some of Massachusetts’s most vulnerable workers. In her letter, she cited a recent investigation by Coakley’s office that found multiple child labor law violations at four Dunkin Donuts franchises resulting in more than $13,000 in fines.

“Now, less than two months later, the House of Representatives passed a bill that rewards the very employers who violated Massachusetts child labor laws. Please do not support a financial race to the bottom for low wage workers in Massachusetts,” Loux wrote.

The bill passed the House on July 18 and was referred two days later by the Senate to the Committee on Ethics and Rules, according to the Legislature’s website.

Last year, Patrick said he was “in favor of the overall bill,” but he eliminated a section of the law that precluded tip-eligible supervisors from having hiring and firing authority, but would allow them to report “workplace infractions” or make hiring and firing “suggestions.” Patrick, in a message to lawmakers, said the differentiation would “likely create confusion, especially as applied to work environments that differ in their staffing models and assignment of duties.”