Washington (CNN) Jared Kushner's proposal to reform the US immigration system has yet to be completed or released, but it's already getting an icy reception from some immigration groups.

For months, President Donald Trump's son-in-law and senior adviser has been chipping away at a plan to overhaul the country's immigration system, seizing an issue that's otherwise belonged at the White House to senior adviser and immigration hardliner Stephen Miller.

Kushner has been meeting with a variety of groups on all sides of the immigration debate and said last week he will present a plan to Trump shortly -- an announcement that has resulted in more queasiness than confidence for those seeking to limit legal immigration.

"We're not expecting to be happy," said Roy Beck, president of NumbersUSA, a group that advocates for reduced immigration.

NumbersUSA was among the groups that participated in meetings at the White House earlier this year about reforming the country's immigration system.

Last week, the group released an ad against keeping immigration levels the same, which is what Kushner's proposal is expected to do, arguing that it hurts American wages.

"Isn't it time to reduce immigration numbers and let wages rise more?" the narrator says in the ad.

During an interview at the Time 100 Summit last week, Kushner said he was putting together "a really detailed proposal" to reform the US immigration system, but did not reveal any of the components of his proposal. He added that he and his team will be presenting the latest version of their proposal to Trump who will likely offer changes.

"The President asked me to work on this topic," Kushner said. "This isn't one of the topics that I came to Washington to work on."

CNN reached out to the White House for comment.

A senior administration official told CNN recently that Kushner will focus on border security and legal immigration.

The border security section would include constructing physical barriers where needed and modernizing ports of entry in the north, south and on the coasts -- so that every person, vehicle and cargo container is scanned to prevent anything illegal from coming into the country, and that trade is facilitated more quickly. This proposal, the official said, would protect rights and respect due process while also preserving the right to detain, adjudicate and remove any individual if need be, especially people trying to circumvent the legal system.

The second part of the proposal asks what legal immigration should look like. With 185 different kinds of visas, the system right now is easy to game, the official said. This proposal would for now keep the level of immigration at the same level it is currently, and work toward a merit-based system based on the Canadian, Australian and New Zealand systems. Trump has previously touted those systems as examples of the direction in which the US should move.

For Jessica Vaughan, director of policy studies at the Center for Immigration Studies -- a group that supports reduced immigration, taking on an all-encompassing approach could sink it before it goes anywhere.

"If we want to implement something that's going to work, it needs to be done in the proper sequence. The urgent problem needs to be taken care of first," Vaughan said, referring to the southern border, which has seen a dramatic increase in the number of people apprehended by the US Border Patrol.

"Our top concerns are that the proposal will try to bite off more than reasonably can be chewed," she added.

The proposal is not faring any better with immigrant advocacy groups who worry that it'll include changes to laws designed to protect migrant children.

At issue are the Trafficking Victims Protection Reauthorization Act, which requires that unaccompanied children not from Mexico or Canada be transferred to government custody and placed in removal proceedings, and the Flores Agreement that dictates how long a child can be held in detention. The Trump administration has sought changes to both, arguing that they encourage migrants to come to the border.

"We feel like children need to be protected at the border, that you need to have a process in place like we do under current law that children are protected," said Kerri Talbot, director of Federal Advocacy at the Immigration Hub, an immigrant advocacy organization.

"We'll be looking out for whether the proposal complies with basic child protection standards: Is it compliant or is this a way to legitimize a way to not comply?" said Michelle Brané, director of the Migrant Rights and Justice Program at the Women's Refugee Commission, which advocates for displaced women and children.

Changes to TVPRA also came up Tuesday during a congressional hearing with Acting Department of Homeland Security Secretary Kevin McAleenan.

"I -- I think that's -- that's something we could discuss with Congress in the context of improving TVPRA to -- to eliminate the double standard that now applies for unaccompanied children coming from contiguous countries, Mexico and Canada, versus non-contiguous countries," McAleenan said.

He added: "We'd like to be able to provide a safe return for them, but it's not provided for right now under the TVPRA. That's something we'd like to work on with Congress."

On the eve of McAleenan's testimony, the White House also released a memo directing the DHS secretary and attorney general to take "all appropriate actions" to toughen the asylum process.

This isn't Kushner's first foray in policy. He also played an instrumental role in criminal justice reform last year that resulted in a groundbreaking prison and sentencing overhaul bill and is one of the main architects of a US Middle East plan.

"I said if I can get Stephen Miller and Kevin Hassett to agree on an immigration plan, then Middle East peace will be easy by comparison," Kushner said.

But attempts at comprehensive immigration reform on Capitol Hill often come up short, given the complex nature of the issue and varying opinions on what the system should look like. The last major attempt at comprehensive immigration reform took place in 2013 under the Obama administration, but was not taken up by the House.

Kushner's proposal hasn't been released and could include provisions that would shore up support from outside groups once it is. But if history serves as evidence, the path forward for an immigration plan won't be an easy one.