Washington (CNN) Acting Homeland Security Secretary Kevin McAleenan on Tuesday defended the Trump administration's actions on the southern border, saying it's now on Congress to fix the problem, while Democrats grilled him on tariff negotiations with Mexico and the state of children separated from their families.

"It's been over 18 months for the administration asked for the legislative fixes that would have prevented the current crisis and 40 days since we asked for the emergency funding necessary to manage it," McAleenan told a Senate panel Tuesday.

During the two hour-plus hearing, senators pointed fingers at the Trump administration and each other for not passing previous legislation designed to assist the southern border.

President Donald Trump started his term with Republican control of the House and Senate and a focus on constructing his signature border wall. During that time, legislation still struggled to move forward and the wall has not made much headway. Since then, the situation along the border has worsened and the House has turned over to Democratic control, making it more difficult to pass legislation.

"This crisis is unlike anything our country has ever faced," McAleenan said, citing a 623% increase in "total enforcement actions" this May compared to May 2017.

The US has been facing a dramatic spike in apprehensions along the southern border. In May, the Border Patrol arrested nearly 133,000 migrants, according to Customs and Border Protection data, including more than 11,000 unaccompanied children. The shift in demographics -- from single adults to families and children predominantly from Northern Triangle countries of Guatemala, Honduras and El Salvador -- has presented its own set of challenges to the Department of Homeland Security.

Senate Judiciary Chairman Lindsey Graham said the breaking point "has long passed" and warned that without resources "there will come a point to where we'll have complete, absolute failure to control, our border, and we are getting there daily."

Graham also acknowledged that a border wall "will not fix this problem."

"The only way a wall would fix this problem is to build it in Mexico, so they never step foot in the United States," he said. "But once you put one foot in the United States and you claim asylum, we have a major dysfunctional system."

McAleenan also conceded that the wall "is for the border security problem," noting that migrants are turning themselves in to Border Patrol agents.

The Senate Appropriations Committee will consider a major funding bill next week, Graham said. The measure will include $3.3 billion for "humanitarian assistance" that will increase shelter capacity for unaccompanied migrant children and the feeding and care of those in custody. It will also include $1.1 billion for "operations support" including funding for more detention beds, he said.

Despite tense exchanges throughout Tuesday's hearing, McAleenan earned praise by lawmakers on both sides of the aisle.

"I hope the President will nominate you to be DHS secretary in a permanent fashion. I cannot think of anybody I have ever met that is more capable of doing the job under difficult circumstances," Graham said at the conclusion of the hearing. McAleenan has not publicly expressed interest in the post.

One to five families separated at border daily

Democrats on Tuesday raised family separation -- an issue for which they've continued to slam the administration. McAleenan said between one and five families were separated under extreme circumstances each day in the one-year period since the administration rolled back its controversial zero tolerance policy at the border that resulted in widespread family separations last year.

"It's a very rare circumstance," McAleenan said. "It happens only for the safety and welfare of the child, when we have a concern about abuse or neglect or there is a communicable disease, an emergency medical issue, or a serious criminal prosecution unrelated to the unlawful border crossing."

Pressed by Democratic Sen. Dianne Feinstein of California, McAleenan could not give a total number of the families separated since June 20 -- when Trump signed an executive order reversing the policy that resulted in systematic family separation -- but said it was about 0.36% of families crossing in the past year, and added that about 1,500 to 3,500 families crossed on average last year.

McAleenan says he's not been asked to do anything illegal

After Democratic Sen. Amy Klobuchar of Minnesota referenced a CNN report that said Trump offered to pardon McAleenan if he was convicted of having border agents block asylum seekers from entering the US, McAleenan said he has not been asked by the White House to break the law.

"No, no one has asked me to do anything illegal," McAleenan said, repeating what he's said in previous testimony. "I've never been asked to do anything unlawful nor would I."

DHS is investigating CBP data breach

McAleenan said his agency is "investigating aggressively" after a data breach of a Customs and Border Protection contractor that handled sensitive traveler data from along the northern border, but called it "not a widespread issue."

"We're talking about a few lanes at a single port of entry, a test for about a month for a month and a half. That's the source of the data. This is not a widespread issue. It's a land border vehicle crossing. It's something they are Investigating aggressively right now and we're going to absolutely disclose our findings and take corrective action," McAleenan said.

He called the investigation a "top priority" and promised an update to Congress in a matter of weeks. No Homeland Security or Customs and Border Protection systems were breached in the incident, he said.

Tariff-immigration talks with Mexico

McAleenan's testimony came amid questions about what exactly the US and Mexico agreed to over the weekend in high-stakes tariffs and border enforcement talks.

The agreement reached by the two countries over the weekend derived from Trump's threat to impose tariffs on Mexico in retribution for, what he argued, was lackluster enforcement by Mexico to stem the flow of migrants. But it's not clear whether the deal will yield the results desired by the President, principally a sharp reduction in the number of migrants illegally crossing the border.

The deal included a pledge by Mexico to do more to curb migration on its southern border, as well as the expansion of a policy that allows the US to return some asylum seekers to Mexico for the duration of their immigration hearings.

Trump has defended the agreement following a New York Times report that said it primarily included pledges Mexico previously made to the US, saying that it would not have happened without the tariff threat and that more of the deal will be revealed in the future.

McAleenan has so far defended the agreement. "People can disagree with the tactics," he said in a Fox News interview Sunday. "Mexico came to the table with real proposals. We have an agreement that if they implement will be effective."

During Tuesday's hearing, McAleenaan also said a safe-third country would be "very effective." The Trump administration has pushed for a safe-third country agreement, which would effectively bar non-Mexican migrants from claiming asylum in the US.

Trump has recently insinuated that there's more to the agreement reached by the US and Mexico that hasn't yet been made public.

Democratic Sen. Richard Blumenthal of Connecticut pressed McAleenan on those details, but the acting secretary dodged in his responses, punting to the President and his statements on the agreement.

Blumenthal appeared to be unsatisfied with the response. "If you are unable to disclose anything more about what's in this deal, I think with all due respect, you are failing in your duty to come before this committee and fully disclose what the commitments of this nation are, with respect to immigration," he said.

McAleenan responded: "Respectfully, I defer to the President's own statements on that matter and the coordination with the government of Mexico."

Graham recently introduced legislation that tries to accomplish much of what the administration has requested.

His bill would, in part, change the current asylum process in three substantial ways: It would require migrants seeking asylum to apply at a consulate or embassy in their home country or in Mexico, instead of at the southern border; it would increase the amount of time that migrant children could stay in custody from 20 days to 100 days; and make it easier for officials to deport unaccompanied minors to Central America.

The measure also calls for 500 new immigration judges to chip away at the massive immigration court backlog.