Lawmakers grappling with ways to keep guns from the hands of the mentally ill are faced with a central question: How to entice states to report such cases without trampling on the Constitution?

Sen. Lindsey Graham (R-S.C.) this week said he’s eying legislation to require states to report cases of severe mental illness to the federal government in hopes of reining in gun violence.

“I’m thinking about that,” he said Thursday. “That’s a 10th amendment deal, but it’s also – I think we’d benefit.”

But even gun-control advocates doubt the federal government has the authority to compel states to share those records. They said Congress can provide financial incentives – both payments and penalties – to encourage such reporting. But a federal mandate would likely prove unconstitutional.