Underscoring the intraparty squabbles hindering the bill, House Republicans meeting in a private conference took the rare step Tuesday evening of voting overwhelmingly to oppose the Senate measure. The tally was 114-23, reflecting what Minority Leader John Boehner, R-Ohio, called Republicans' "significant concerns" with the legislation.

Utah's two Republican senators were split on Tuesday's vote, with Sen. Bob Bennett supporting the renewed debate and Sen. Orrin Hatch opposing it.

Hatch expressed concerns about provisions such as the proposed "Z visa," saying it "creates more problems than it tries to fix."

The Z visa would legalize undocumented immigrants who arrived after Jan. 1, 2007, if they pass a background check and pay fees and fines. It would also, if they meet additional requirements, allow them to earn permanent residency.

"I voted against the last immigration 'solution' in 1986," Hatch said in a statement. "It failed, and this one, in some respects, is worse."

Bennett, meanwhile, said in a statement that he hasn't decided whether or not he'll vote for the final version of the bill, but that he looks forward to "a thorough debate on immigration, including a provision I support that will increase funding for border security by $4.4 billion."

Bennett was referring to the bill's security triggers such as adding 20,000 border agents, 370 miles of fencing and a new system to prevent hiring illegal workers.

Gov. Jon Huntsman Jr., led a renewed call by the Western Governors' Association, for the Senate to pass reform, along with Arizona Gov. Janet Napolitano.

Huntsman's spokeswoman Lisa Roskelley said while it remains to be seen what the final bill will look like, "We are supportive of the legislation and looking forward to seeing the end results."

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Contributing: Deborah Bulkeley and Suzanne Struglinski, Deseret Morning News.