The union has asked the Ministry of Health to issue a letter which protects nurses from repercussions if they voice concerns over patient safety.
NDP Leader Cam Broten backed the demand for the letter, and called for an investigation into the matter.
Union president Tracy Zambory said Friday she receives calls daily from nurses who are afraid to come forward with concerns about Lean, the name of the program.
Zambory has said that nurses hoped that Lean concepts would be effective, but it's been disappointing.
Health Minister Dustin Duncan says they have always encouraged nurses to share concerns.
Premier Brad Wall has defended Lean, saying it has already paid for itself with savings on two new hospital designs and with ways to reduce wait times.
But Zambory said the program, while it sounds good in principle, does nothing to address patient safety.
"Registered nurses are the ones who are with the patients who come into the health care system regardless where they enter the most and we're the ones who have to speak out to say this is not working."
She also said nurses are reporting they are being intimidated to not speak out.
"They are being told that their social media is being monitored by managers so they better watch their steps," Zambory said Friday.
"It seems like because we are sounding the alarm to say that Lean works good in some areas but in patient care we have problems and we are being summarily shut down, there's a problem."
The Health Ministry says they are considering issuing the letter.
Opposition NDP Leader Cam Broten has said that province paid $3,500 a day for Japanese sensei to teach Lean techniques and questioned why the program includes Japanese cultural training.
"I am horrified to hear how nurses and front-line health care workers are being treated within this government's Lean experiment," Broten said in a statement issued Friday.
"When they're being warned not to identify problems because it doesn't fit with the government's pro-Lean messaging, that absolutely sounds like a cult. Shutting down a nurse who has identified a patient safety concern is dangerous and wrong. Threatening a nurse who wants to advocate for better health care is very disturbing."
Lean was originally created in the manufacturing sector, but has since been applied to many other sectors and industries.
Saskatchewan is the first jurisdiction in Canada to apply the Lean program across its entire health system.
(CKRM, The Canadian Press)