Republican senators have made no secret of their desire to moderate Medicaid cuts approved by the House in its bill to deliver President Trump’s agenda.

Now they are preparing to change a provision that would cut deeply into another central pillar of the nation’s safety net: the Supplemental Nutrition Assistance Program, formerly known as food stamps, which provides food benefits to low-income families.

Senators from states reliant on the program worry that the changes the House pushed through — particularly one that would have states assume some of the cost of assistance payments currently paid entirely by the federal government — will punt huge costs onto their states. And they worry that the changes could also result in the loss of free school meals for young low-income children.

It is yet another policy dispute between the two chambers that could complicate efforts to ultimately pass a final, compromise version of Republicans’ marquee legislation. Hard-liners in the House have said that they only reluctantly voted to pass what Mr. Trump refers to as his ”big, beautiful bill” and will not support legislation with fewer spending reductions.

But in the Senate, where Republicans represent entire states, not districts, the SNAP provisions have prompted alarm.

The two senators from West Virginia, Jim Justice and Shelley Moore Capito — both Republicans — have expressed concerns about how the House provisions will hit their state, where one in six residents receive food assistance through the program. Their governor, Patrick Morrisey, also opposes the plan.