A proposal for the Cook County Jail to free some inmates wanted by immigration authorities could be up for a vote at the county board meeting Wednesday morning. But it’s hitting turbulence.

Board Commissioner Timothy Schneider, R-Streamwood, plans to speak against the measure at the meeting. “Are we going to disregard the rule of law?” he said Tuesday afternoon. “If they’re illegal they should be deported.”

On an average day, the county turns over three inmates wanted by Immigration and Customs Enforcement. Those transfers follow ICE requests, known as detainers, that ask the jail to hold the inmates up to two business days beyond what their criminal cases require.

Under the proposed ordinance, the county would start freeing the inmates unless the federal government paid for the hold. County Board President Toni Preckwinkle and nine commissioners are sponsoring the measure.

Preckwinkle said Tuesday that asking local jails to hold inmates for suspected immigration violations amounts to an unfunded federal mandate. “It costs us $142.80 a day to keep somebody in the jail,” she said. “It adds up over time.”

Sheriff Tom Dart has criticized the holds but his spokesman, Steve Patterson, said Tuesday afternoon the proposed ordinance deserves more debate: “We’d just like more dialogue with all parties in the room.”

Patterson said those parties include federal authorities, local law-enforcement officials and immigrant families and their advocates.

Lauren Chooljian‎ contributed to this report.