Washington (CNN) Lawmakers on both sides of the aisle grew frustrated with the Trump administration Tuesday on immigration, repeatedly pressing government officials for more specifics and realistic goals.

Senators were questioning officials from the Department of Homeland Security and Department of Justice at a hearing about Deferred Action for Childhood Arrivals, an Obama administration program protecting young undocumented immigrants brought to the US as children, which President Donald Trump has chosen to end.

It quickly became clear that the Senate judiciary committee members present were dissatisfied by the officials' answers, as well as the administration more broadly, as Congress tries to come up with a solution for the hundreds of thousands of immigrants in limbo before March, when DACA permits will start expiring.

"I'm looking for a little more meat on the bones," said Louisiana Republican Sen. John Kennedy during a lengthy back-and-forth pressing DHS for specifics. "Tell me, if you would, sir, what the Trump administration would like us to do with respect to so-called Dreamers?"

The target of his questions, DHS Assistant Secretary Michael Dougherty, gave a general outline of what Trump would like to see, including a resolution for DACA recipients, border security, stronger deportation authority, enhanced vetting of immigrants, overhauling some visas and transforming the immigration system to favor high-skilled immigrants.

But Kennedy wasn't satisfied.

"Let me answer it this way," Dougherty began, with Kennedy cutting him off.

"How about you just answer it?" Kennedy said, continuing to ask Dougherty under which conditions DACA recipients should be allowed to stay in the US.

"I don't have those details for you, sir," Dougherty said.

The hearing revealed how much interest there is in Congress for some sort of deal on immigration and DACA -- and also how deep the divisions between parties remain.

Little consensus was achieved by the hearing over what a specific deal should like, and the Kennedy exchange typified many of the interactions between the senators and the witnesses, which happened with both Republicans and Democrats.

Illinois Sen. Dick Durbin, a Democrat, and North Carolina Sen. Thom Tillis, a Republican, have both sponsored legislation that would provide a permanent pathway to citizenship for DACA-eligible immigrants, with slightly different approaches. Both also expressed frustration with Dougherty's list of the administration's priorities.

Durbin referenced his efforts to write comprehensive immigration reform legislation in 2013 that passed the Senate on a large bipartisan basis, but died in the House. He noted more than 500 amendments were offered, quipping "the most prolific person to offer amendments is our current attorney general."

"We addressed virtually every issue that you mentioned in your long list as part of comprehensive immigration reform," he said, referring to Dougherty's response to Kennedy. "I hope the administration doesn't use your list ... Your list was the entirety of the comprehensive immigration reform."

He said it was "too much" to "put the burden" on a DACA bill to answer all of the questions.

"It's too much to ask ... and I hope you'll take that message back," Durbin said.

He got backup from his Republican colleague, Tillis, who used five minutes of questioning to deliver a statement to the gathered officials, instead.

"I know you can't get into the President's head, but that's one of the benefits of social media and tweets," he said, proceeding to read aloud most of the President's tweets about DACA.

Tillis said it was clear to him that Trump was interested in a deal with border security and compassionate response to DACA, rather than everything Dougherty listed.

"It reads like a laundry list for comprehensive immigration reform, and if Congress has proven an extraordinary ability to do anything, it's to fail at comprehensive immigration reform," Tillis said. "We know what the problem is, we know what a reasonable solution is, and we should provide it."

There were other tense exchanges as well, including from the former top Democrat on the committee, Vermont Sen. Pat Leahy, who especially took issue with the Justice Department representative. At the outset of the hearing Chairman Chuck Grassley noted that DOJ had not submitted written testimony for the hearing, and acting Assistant Attorney General Chad Readler, of the civil division, said he was limited in speaking outside of what was already public because of ongoing lawsuits over the administration's termination of DACA.

Leahy pressed Readler on Attorney General Jeff Sessions' letter about the rescission of DACA, which suggested lax immigration enforcement was responsible for crime, violence and even terrorism.

"Can you provide this committee with any examples of Dreamers being involved in terror activity? ... You don't have to give me hundreds, just give me one!" Leahy said, raising his voice.

"I'm not aware of any examples," Readler said.

"Neither is the attorney general when he said that," Leahy said.

After further back-and-forth about what Sessions meant, Readler noted he would be testifying before this committee himself this month.

"He's taken longer than any attorney general since I've been here, but I've only been here 42 years," Leahy said.

Under questioning from Republican Sen. Lindsey Graham, of South Carolina, who has co-sponsored Durbin's bill, the DHS officials did say they supported a pathway to citizenship for DACA-eligible individuals in an eventual solution -- and said they were largely the type of people the US should want.

"They're a benefit to the country as are many immigrants coming in," Dougherty said. "They are a valuable contribution to our society, we need to regularize their status through legislative means."

He also said DHS did not support the notion of creating a permanent visa status that would never allow people to be naturalized -- saying the White House would be of the same mind.

"I think creating second-class citizens or people who are never able to naturalize is not a good model," Dougherty said, adding "I do" when asked if he thinks the President agrees.