“I think most Americans assume that ICE agents and officers are empowered by our government to enforce the law,” Crane said. “Nothing can be further from the truth. With 11 million illegal aliens in the U.S., ICE agents are now prohibited from arresting illegal aliens solely on charges of illegal entry or visa overstay, the two most frequently violated sections of U.S. immigration law.”

The Obama administration announced in December that illegal immigrants who are arrested in minor crimes no longer will be targeted for deportation.

Vargas emotionally told his story of coming to America when he was 12 and learning that he was undocumented when he tried to get a driver’s license. Sitting in front of his Filipino-American family, which included his uncle Conrad Salinas, who served in the U.S. Navy for 20 years, he told of his mother’s decision to send him to the U.S. so he could have a better life. A crowd of undocumented immigrants in the audience cheered when he told the senators that he had questions for them.

“What do you want to do with me?” he said. “For all the undocumented immigrants who are actually sitting here at this hearing, for the people watching online, for the 11 million, what do you want to do with us?”

Chairman Patrick Leahy, D-Vt., described a “growing consensus” among Democrats and Republicans and questioned those who demand more enforcement.

“I fear they mean ‘enforcement only,’” Leahy said. “To them I say that you have stalled immigration reform for too long. We have effectively done enforcement first and enforcement only. It is time to proceed to comprehensive action.”

Sen. Jeff Sessions, R-Ala., countered that the existing proposals sound more like “amnesty-only.”

Murguia acknowledged the concerns of some Republicans after the hearing but said she was encouraged by another Republican, Graham, who re-emphasized the progress made on the border.

“This is not going to be a cake walk,” Murguia said. “We have a lot of hard work to do.”

Rubio, who was not at the hearing, issued a statement later saying much was left to be done on the border and stressing “security triggers” in the proposal he’s helping to craft.

“If we are going to pass bipartisan immigration reform this year, the administration must accept the principle that security triggers must be met before anyone who is currently undocumented is allowed to apply for a green card,” Rubio said in the statement. “Secretary Napolitano’s refusal to accept this bipartisan principle at today’s Senate hearing is discouraging for those of us who are serious about permanently fixing America’s immigration system.”