Devious. Disturbing. Underhanded. Sneaky.

These are among the adjectives that advocates for welfare recipients are using to describe Gov. Charlie Baker's decision to reject a change that would expand welfare benefits for children unless the Legislature agrees to another change that would cut thousands of children off from welfare.

"This is an unconscionable choice he's forcing on the Legislature, and the way he did it is devious," said Deborah Harris, a senior staff attorney at the Massachusetts Law Reform Institute, which practices poverty law.

In the state budget, the House and Senate agreed to lift the "family cap," a cap that denies additional welfare benefits for children born while a family is already receiving welfare.

Welfare benefits are based on family size. There are an estimated 8,700 children in Massachusetts who were born after their families were already getting welfare payments, so their family's payments do not reflect their birth.

Many states instituted caps around the time of federal welfare reform in 1996 in order to discourage women on welfare from having more children, then applying for larger benefits. Advocates for repealing the cap say women do not decide whether to have a child based on a $100 monthly addition to their welfare check, and the result of the cap is the entire family suffers with less money.

But when Baker signed the state budget on Thursday, he did not sign the family cap lift. Instead, he returned it to the Legislature with an amendment.

That amendment would lift the family cap but also change welfare eligibility laws so that an adult's Supplemental Security Income is counted when determining if a family is eligible for welfare. SSI is a federal payment given to severely disabled adults.

Baker wrote in his amendment letter, "Eliminating the 'family cap' without other accompanying changes could have the perverse effect of reducing incentives for TAFDC recipients to get back to work, and cause existing inequities in the TAFDC program to persist and expand." TAFDC is an acronym for Transitional Aid to Families with Dependent Children.

Asked about the change, Baker called it a "reasonable compromise" to "level the playing field" around benefits associated with various federal programs. For example, he said veterans' benefits are counted in determining eligibility for welfare.

Former Gov. Deval Patrick did something similar in 2009, effective in 2010. The Patrick administration started counting SSI income for welfare eligibility, without legislative approval, as part of a strategy to reduce the deficit.

Baker has proposed counting SSI income for welfare eligibility twice previously, in 2016 and 2017. According to state figures as of last year, 5,200 children with a severely disabled parent would lose their welfare benefits entirely under the change, and 2,100 children would lose part of their benefit.

The Legislature rejected the change both times and added language into the budget explicitly prohibiting the Baker administration from making the change unilaterally.

Harris called it a "poison bill" that Baker stuck into the family cap amendment.

Naomi Meyer, an attorney at Greater Boston Legal Services, said, "We're deeply disappointed that he would try to make repeal of the welfare family cap contingent on making cuts to other vulnerable children who need welfare."

Meyer said the governor did not propose making the SSI change during the normal legislative process this year. "We see this as a rather underhanded attempt to shove it through at the last minute after it has not been vetted this year," Meyer said.

"We do think it's a sneaky move," Meyer said. "He knows that the Legislature has rejected his proposal to count SSI because it would harm vulnerable families."

Baker also vetoed the budget language that prohibits his administration from making the change to eligibility unilaterally. The Legislature can override that veto.

But lawmakers are in a more difficult position with regards to the family cap, because they got the budget to Baker so late. When Baker returns a policy section with an amendment, the Legislature must vote on it as if it is a new bill. The governor then has another 10 days to sign or veto it.

So if the Legislature decides to pass the family cap without the SSI eligibility change, Baker can simply wait 10 days and veto it. The legislative session ends July 31, so lawmakers will no longer be in session to override his veto.

"It was very clever," said Rep. Marjorie Decker, D-Cambridge, who sponsored the amendment to lift the family cap. "The governor has been determined for years to reduce potential benefits for people on SSI."

Decker said it is "disturbing" that while the Legislature reversed a policy that hurts poor families, "the governor would find a way to insert another goal that is about reducing resources to those that need them the most."

"We're talking about the people who have the least among us," Decker said. "The question is not how to reduce their benefits, because that's what he's doing, it's how to evaluate do they have enough of what they need. The answer to that is no."

Carol Rose, executive director of the ACLU of Massachusetts, noted that on Friday Baker signed a bill eliminating archaic abortion laws, a day after "he took action to make poor women more economically vulnerable."

"The juxtaposition is ironic and ugly," Rose said. "We hope the Legislature stands up and finds a way to swiftly right this wrong."

Decker said the Legislature will find a way to lift the family cap, but the timeline and method is still to be determined.

House Speaker Robert DeLeo, D-Winthrop, said he is disappointed that the budget delay led to an inability to override Baker's veto. He suggested that if the cap does not get lifted this session, lawmakers could take it up again next session, which begins in January, as a standalone bill.

This story was updated to note that Patrick did something similar.