A St. George lawmaker has put on hold a debate on an omnibus piece of immigration legislation as he continues to work to make it palatable to religious and business organizations.

Describing the planned changes to SB81 as "word-smithing here and there," Sen. Bill Hickman, R-St. George, said he wants to make the bill "a really fine piece of legislation."

The Senate vote has been rescheduled for Thursday morning. The bill would create barriers against undocumented immigrants obtaining jobs or public benefits.

Lane Beattie, president and chief executive officer of the Salt Lake Chamber of Commerce, said he's involved in an ongoing discussion with Hickman about potential support for SB81 but said "there would have to be changes."

The chamber is part of a coalition of business, nonprofit and religious groups that has endorsed another measure, SB97, which would create a task force to study the immigration issue.

"We believe a study is very, very positive," Beattie said. Still, he added, the chamber's support for SB81 is a possibility.

That possibility started, Beattie said, when Hickman amended the bill to remove "critical" provisions that would have repealed a law allowing undocumented immigrants to pay in-state tuition and that would have required high rates of income-tax withholding for some employers.

Hickman pointed to tweaking a provision on who can be issued identification as an example of the changes he has in mind.

Senate President John Valentine, R-Orem, said Hickman has done a good job balancing compassion with the rule of law as he's crafted his legislation by "hitting at the core but rounding off the edges."

Valentine said that the bill likely has enough support to pass the Senate, but not a veto-proof majority.

Gov. Jon Huntsman Jr. "has expressed reservations about some legislation regarding immigration in their current form," and while meeting with Democratic lawmakers Tuesday said he'd contemplate vetoes, said Lisa Roskelley, the governor's spokeswoman. Specific details weren't discussed, she said, and the governor had indicated he hoped work would be done to make those bills useful legislation.

Hickman said he hoped the governor would "consider the fact that citizens of this state overwhelmingly want something done."

Hickman also said he's been working to satisfy the concerns of religious leaders, including those of The Church of Jesus Christ of Latter-day Saints.

To that end, Hickman said he plans to modify a provision creating a class A misdemeanor for harboring or transporting undocumented immigrants to ensure it doesn't prevent churches from performing their normal duties.