Washington (CNN) The eye-popping numbers of potential new citizens and billions for border security got most of the attention when President Donald Trump's immigration proposal landed Thursday.

But while the noise about the "amnesty" for "wall" trade was the loudest, it obscured what actually would be a much more difficult fight: the President's proposed sweeping changes to the immigration system.

The Trump administration briefed reporters and supporters on its proposal Thursday : offering a pathway to citizenship for an estimated 1.8 million undocumented immigrants who came to the US as children and asking for $25 billion for border security including infrastructure.

If that were all that was on the table, a deal might already be at hand. In fact, Democrats were mostly prepared to agree to such a proposal, which could have lined up some moderate Republicans as well.

But the deal also included two other "pillars," as the White House has called them: family-based migration and the diversity visa lottery. In addition, the administration proposal included a number of "legal loopholes" it wants to close in the border security pillar beyond physical security -- a repackaged effort to expand federal immigration authorities.

Taken together, those efforts would amount to a dramatic reshaping of the legal immigration system -- one that will be far more complicated to negotiate on Capitol Hill.

Senate Majority Whip John Cornyn of Texas agreed Thursday before the White House announcement that the elements of the deal beyond pure border security were arguably more complicated.

"I think they probably are," he said, adding that with more understanding he thought they could be negotiable.

Democratic Sen. Tim Kaine of Virginia, who is part of a bipartisan Senate group working to find common ground on the issue, had said earlier Thursday that while a full border wall is not acceptable, a major investment in border security is.

"I trust big investment. I've voted for that already," Kaine said. "When you can patrol a border better with drones and sensors, the wall may not be the best way. But that we would make a big investment in it? The Dems are there already."

GOP Sen. Mike Rounds of South Dakota said the issue of family migration comes up if the undocumented population covered by the bill is granted citizenship -- and that leads down a difficult road.

"if you do that, you have to address the issue of chain migration, and that's where it becomes a lot more complicated. So we've got our work cut out for us," Rounds said upon leaving the morning bipartisan meeting.

Thorny proposals

The White House proposal would limit family sponsorship to spouses and minor children, eliminating a number of existing categories including adult children, both married and unmarried; parents of adult US citizens; and siblings of adult US citizens. Experts have estimated that cutting these categories would reduce the roughly 1 million green cards given out yearly by 25% to 50%.

At first, the Trump proposal would use the green cards from the eliminated categories -- plus the 50,000 from the eliminated diversity visa lottery -- to work through a backlog of millions of people waiting in a line upward of 30 years long for their green cards. The bill does extend an olive branch to the left in not making the cuts retroactive -- meaning anyone already in line would still be eligible. Groups on the right are outraged that the plan would mean potentially 10 to 20 years before cuts to immigration begin.

But Democrats are unlikely to accept such a sweeping cut in legal immigration at all. And cutting the diversity visa lottery is not as straightforward as some believe -- especially to members of the Congressional Black Caucus and other affinity caucuses, who are vocal about the importance of immigration from lesser represented countries

And the framework includes vague references to closing "legal loopholes," as a White House official put it on a briefing call, as part of the border security pillar -- perhaps one of the biggest poison pills of the deal.

The White House released only a top-line overview of what it was seeking -- what it characterized as "closing the loopholes" to more easily detain and deport immigrants. But a document obtained by CNN that goes into more detail, which the Department of Homeland Security has been providing to lawmakers in meetings, and the descriptions released by the White House suggest it will pursue aggressive changes.

In addressing "catch-and-release," as the White House put it, the framework could allow detaining individuals indefinitely as they await deportation for months and years -- something that has been curtailed as the result of constitutional concerns from courts. The proposals could also vastly expand the definitions of criminal offenses that could subject an individual to deportation.

All the efforts to more aggressively deport and reject undocumented immigrants could be anathema to Democrats and some moderate Republicans.

"I am a lot less interested in things that have the effect of distorting family relationships or splitting up families, and border security is less likely to do that," said Democrat Michael Bennet of Colorado, who has long pursued an immigration compromise.

"It's crazy," said Democratic Sen. Cory Booker of New Jersey. "This is not an easy negotiation, but we should move on the things we all agree on."

Support for a simpler deal

The realities of trying to sort through the complicated issues the White House is looking to attach to a deal on the expiring Deferred Action for Childhood Arrivals program are leading lawmakers on both sides of the aisle to suggest paring down the negotiations to just two pillars: DACA and physical border security.

"We all need to understand that there are two things that are critical," Sen. Heidi Heitkamp, a North Dakota Democrat, said as she was leaving the bipartisan group. "Dealing with the Dreamers, because we're up against (a) March deadline, and dealing with border security. We all agree we need border security. We need more definitional work done on border security."

Kaine agreed, saying there's a need to be realistic.

"There's all kinds of issues I want to fix, I just think it's probably going to be easier to start with the two pillars," he said.

Republican Sen. Lamar Alexander of Tennessee, one of the leading forces in the bipartisan group, was also vocal about a narrow approach.

"We don't have to solve the entire problem of legal immigration in this bill," Alexander told CNN. "All we really have to do is focus on the young people who were brought here illegally through no fault of their own, and border security. Sometimes taking small steps in the right direction is a good way to get where you want to go."