Massachusetts Governor Charlie Baker says he’s amenable to delaying new eligibility requirements for a state health care program that pays for uninsured and under-insured residents.

The Baker Administration says changes scheduled to go into effect this Friday would save the Health Safety Net Program about $60 million by, among other things, reducing income levels and enforcing existing rules. But critics, including some lawmakers, say that could further reduce access to healthcare for the working poor.

Speaking in Springfield, Governor Baker called the changes necessary for the program’s integrity.

“But I’m perfectly happy to, as we usually are, to work with the legislature on making sure that we don’t do something that they or others view as disruptive,” says Baker.

Lawmakers are considering an amendment to a budget bill that would keep current eligibility standards in place until June 30th.