CONCORD, N.H. — Supporters of a bill that would offer up to six weeks of paid leave for private-sector New Hampshire employees to care for a new baby or a relative with a serious illness made one last push Wednesday to save the legislation as it faces an uncertain future.

Early recommendations indicate Senate lawmakers may send the bill back to a committee. The tactic often is used as a way to effectively kill legislation.

Dozens of residents gathered at the Statehouse to share stories on how the lack of paid family medical leave has affected their lives in a plea to legislators who will be deciding the bill’s fate Thursday.

“Our utilities were shut off. Our refrigerator was bare, and our arms were empty. We were never able to give Sawyer a proper funeral,” said Nancy Glynn, a mother from Manchester, who said that paid medical leave would have helped after the loss of her child.

Nikki Casey, of Nashua, who has struggled with addiction, said a family and medical leave insurance program would be a critical tool in combatting New Hampshire’s opioid crisis.

“My recovery would have been a lot easier if I had been able to take the time I needed to get better without the fear of losing my job and the income I rely on,” said Casey, who is now the director of a recovery center.

Supporters say the program is also essential to strengthen the state’s workforce and care for an aging population.

But opponents have argued it’s unsustainable and there remain too many questions. Republican Gov. Chris Sununu came out against the plan, saying more research is needed.

Amid fears the proposal will be tabled, supporters hoped their presence Wednesday would put pressure on lawmakers to reconsider the plan. Many dismissed the idea of studying the proposal as a ruse to kill off the plan.

“I urge the Senate to let these stories drive their policy,” said Amanda Sears, director of the Campaign for a Family Friendly Economy, a group that campaigns for working families’ rights. “This bill would help families when they are experiencing the joy of welcoming a newborn into their lives, or the heartbreak of helping their spouses through their last days.”