SALT LAKE CITY — While shaking Gov. Gary Herbert's hand, kindergartner Alex Navarro delivered a message: "I don't want to separate families."

"I don't want to either," Herbert replied.

Alex was among a dozen children of undocumented immigrants and several adults who showed up outside the governor's office hoping to hand him letters condemning the enforcement-only illegal immigration bill lawmakers passed last week. Herbert emerged from his office for a few minutes to greet the youngsters and listen to what they had to say.

Children weren't the only ones bending the governor's ear over illegal immigration Tuesday. About 90 Republican delegates furious over the Legislature's passage of a guest worker bill arranged an audience with him later that day. They want him to veto HB116 because they say it grants amnesty to illegal immigrants.

Utah County delegate Brandon Beckham, who organized the meeting, said afterward Herbert listened, "but I don't know if he has the will to do what is right."

Going against the will of delegates, he said, would spell "political suicide" for Herbert.

"We won't support the governor if he signs the bill. We won't support him in an election. We won't support him in a convention," Beckham said.

While Herbert didn't mind reporters watching him interact with the children, his staff asked Beckham to escort the media from the room before he arrived.

Applause could be heard several times during the 30-minute meeting. Beckham said it was for delegate comments, not anything Herbert said. He "danced around a lot," Beckham said.

Delegates said Herbert made no promises. His spokeswoman, Ally Isom, said the governor will carefully study the bills before making a decision.

"I think he's going to sign it either way," said Dan Deuel, a GOP delegate from Ogden.

Both delegates and the children who met with Herbert want the same thing but on different bills.

"My grandpa really likes you. So I think you are a good guy. Please don't sign HB497 because it will hurt my community," 8-year-old Cuouhtemoc Barrientos read to the governor from his handwritten letter.

"I applaud you for being involved and letting me know your feelings," Herbert told the children. "We're trying to decide right now what to do."

Those message were among several about illegal immigration in Utah delivered Tuesday. Another group launched an e-mail campaign against a state guest worker program, while Utah Attorney General Mark Shurtleff was in Washington, D.C., touting the Utah Compact and the state's comprehensive approach to the issue.

Herbert has on his desk a package of illegal immigration bills the Legislature approved late Friday. In addition to enforcement and a guest worker program, they call for a migrant worker partnership with Mexico and employee verification and employer sanctions.

That package grew by one Tuesday. Lawmakers have now approved HB469 which allows Utahns to sponsor immigrants to live, study or work in Utah. Immigrants would have to undergo background and health screenings. The sponsor would be financially responsible for the individual. Legislative attorneys say the program is unconstitutional because only the federal government can admit people into the country.

HB497 requires police to check the immigration status of people they arrest for felonies and serious misdemeanors. Officers may check the status of those suspected of less serious misdemeanors.

Latinos, both legal and illegal, are "very fearful" of what the law might do, said Santiago Dirzo, of United for Social Justice, which brought the children to the Capitol. "Now they have to look over their shoulder to make sure they're not discriminated against," he said.

While Herbert met with the children, Utah Rising, a group of tea party activists opposed to the guest worker program, plotted their strategy in a boardroom across the hall from his office. They also want the governor to veto HB116.  They're mounting an e-mail campaign to get his his attention.

"The bottom line is that this bill is so inherently flawed that it cannot be fixed," said Ron Mortensen, founder of the Utah Coalition on Illegal Immigration.

He contends those committing felonies such as gang members and drug dealers who haven't been convicted would be able to obtain guest worker permits.

According to the bill, illegal immigrants would have to undergo a criminal background check and pay up to a $2,500 fine to obtain a guest worker permit that would be good for two years. The bill does not provide a pathway to citizenship. Legislative attorneys say it is unconstitutional. The program needs federal approval and is not scheduled to take effect until July 2013.

Also Tuesday, Shurtleff made presentation on the Utah Compact at a national attorneys  general conference and to U.S. Attorney General Eric Holder. Shurtleff wants to drum up support for a national compact.

Shurtleff said in a telephone interview that it was hard to tell how his words were received. "I've got some work to do, I'll tell you that. Mostly with my Republican colleagues."

The compact outlines principles for civil discussion on immigration reform. It urges federal solutions and policies that don't unnecessarily separate families. Several states have patterned their own compacts after it.

Shurtleff said Holder sounded interested in the concept and appreciated Utah wanting to work with the federal government on immigration issues. Shurtleff also has meeting with the White House intergovernmental affairs staff Wednesday to discuss the state's approach, including the migrant worker partnership he plans to form with Nuevo Leon in Mexico.