House Republican leaders face many decisions regarding details of a tax overhaul but perhaps none more immediately consequential than whether to roll the dice and try to eliminate the state and local tax, or SALT, deduction.

House Ways and Means Chairman Kevin Brady of Texas and Speaker Paul D. Ryan have made it abundantly clear they’d prefer to get rid of the deduction, which allows taxpayers to deduct what they pay in state and local property taxes and either state income taxes or sales taxes.

But if Brady and Ryan move forward with their plan to cut the SALT break from the code, they risk losing support from Republicans from high-tax states such as New York, New Jersey, California and Illinois, more than enough to sink the bill.

“I still believe that the current state and local tax deduction is double taxation at its worst,” Brady said Thursday. “People are taxed locally and then every American — poor, middle-class, otherwise — whether they itemize or not, pays artificially higher federal taxes so some can get a tax break.”

Ryan, a Wisconsin Republican, made a similar comment at a Heritage Foundation event earlier that day, saying, “I would argue we’re propping up profligate, big government states and we’re having states that actually got their act together pay for states that didn’t. I think Wisconsin versus Illinois.”