WASHINGTON, DC - MAY 14: U.S. President Donald Trump waves as he walks toward Marine One before departing from the White House on May 14, 2019 in Washington, DC. President Trump is traveling to Louisiana.  (Photo by Mark Wilson/Getty Images)
PHOTO: Mark Wilson/Getty Images North America/Getty Images
WASHINGTON, DC - MAY 14: U.S. President Donald Trump waves as he walks toward Marine One before departing from the White House on May 14, 2019 in Washington, DC. President Trump is traveling to Louisiana. (Photo by Mark Wilson/Getty Images)
Now playing
02:04
Kushner pushing plan to overhaul US immigration system
FBI Director Christopher Wray testifies before the Senate Judiciary Committee on the January 6th insurrection, in the Hart Senate Office Building on Capitol Hill in Washington, DC on March 2, 2021. (Photo by MANDEL NGAN / POOL / AFP) (Photo by MANDEL NGAN/POOL/AFP via Getty Images)
PHOTO: MANDEL NGAN/POOL/AFP via Getty Images
FBI Director Christopher Wray testifies before the Senate Judiciary Committee on the January 6th insurrection, in the Hart Senate Office Building on Capitol Hill in Washington, DC on March 2, 2021. (Photo by MANDEL NGAN / POOL / AFP) (Photo by MANDEL NGAN/POOL/AFP via Getty Images)
Now playing
02:55
Watch FBI director debunk conspiracy theories pushed by Trump supporters
abrams
PHOTO: CNN
abrams
Now playing
00:51
Abrams on voting rights: We're fighting to protect our democracy from domestic enemies
Goya Foods President Robert Unanue speaks at a press conference with Carlos Vecchio, the Venezuelan Ambassador who is recognized by the United States on December 21, 2020 in Doral, Florida. The two held the press conference to discuss details of a recent shipment of humanitarian aid to Venezuela, donated by Goya Foods. (Photo by Joe Raedle/Getty Images)
PHOTO: Joe Raedle/Getty Images
Goya Foods President Robert Unanue speaks at a press conference with Carlos Vecchio, the Venezuelan Ambassador who is recognized by the United States on December 21, 2020 in Doral, Florida. The two held the press conference to discuss details of a recent shipment of humanitarian aid to Venezuela, donated by Goya Foods. (Photo by Joe Raedle/Getty Images)
Now playing
03:24
Goya CEO under fire for false Trump election claims
Rep. Adam Kinzinger (R-IL) speaks to CNN's Alisyn Camerota about why he thinks that the Republican Party will move on from former President Donald Trump.
PHOTO: CNN
Rep. Adam Kinzinger (R-IL) speaks to CNN's Alisyn Camerota about why he thinks that the Republican Party will move on from former President Donald Trump.
Now playing
02:03
Kinzinger: Trump is a loser and we will move on
Now playing
04:17
NYC mayor says Gov. Cuomo should resign if allegations are true
NEW YORK, NY - JULY 23: New York Gov. Andrew Cuomo speaks during the daily media briefing at the Office of the Governor of the State of New York on July 23, 2020 in New York City. The Governor said the state liquor authority has suspended 27 bar and restaurant alcohol licenses for violations of social distancing rules as public officials try to keep the coronavirus outbreak under control. (Photo by Jeenah Moon/Getty Images)
PHOTO: Jeenah Moon/Getty Images
NEW YORK, NY - JULY 23: New York Gov. Andrew Cuomo speaks during the daily media briefing at the Office of the Governor of the State of New York on July 23, 2020 in New York City. The Governor said the state liquor authority has suspended 27 bar and restaurant alcohol licenses for violations of social distancing rules as public officials try to keep the coronavirus outbreak under control. (Photo by Jeenah Moon/Getty Images)
Now playing
02:29
NYT: Third woman comes forward against Gov. Andrew Cuomo
WASHINGTON, DC - MAY 25: U.S. President Donald Trump and first lady Melania Trump depart the White House for Baltimore, Maryland on May 25, 2020 in Washington, DC. The Trumps will attend a Memorial Day ceremony at the Fort McHenry National Monument and Historic Shrine despite objections by Baltimore Mayor Bernard C. "Jack" Young, whose residents remain under a stay-at-home order due to the coronavirus. (Photo by Sarah Silbiger/Getty Images)
PHOTO: Sarah Silbiger/Getty Images North America/Getty Images
WASHINGTON, DC - MAY 25: U.S. President Donald Trump and first lady Melania Trump depart the White House for Baltimore, Maryland on May 25, 2020 in Washington, DC. The Trumps will attend a Memorial Day ceremony at the Fort McHenry National Monument and Historic Shrine despite objections by Baltimore Mayor Bernard C. "Jack" Young, whose residents remain under a stay-at-home order due to the coronavirus. (Photo by Sarah Silbiger/Getty Images)
Now playing
02:10
Trump got vaccinated in secret. Here's why this matters
Kinzinger
PHOTO: CNN
Kinzinger
Now playing
03:55
Republican lawmaker reacts to being on Trump's 'enemies list'
Former Ambassador to the United Nations Nikki Haley speaks during the first day of the Republican convention at the Mellon auditorium on August 24, 2020 in Washington, DC (Photo by Olivier DOULIERY / AFP) (Photo by OLIVIER DOULIERY/AFP via Getty Images)
PHOTO: Olivier Douliery/AFP/Getty Images
Former Ambassador to the United Nations Nikki Haley speaks during the first day of the Republican convention at the Mellon auditorium on August 24, 2020 in Washington, DC (Photo by Olivier DOULIERY / AFP) (Photo by OLIVIER DOULIERY/AFP via Getty Images)
Now playing
04:41
Haley flip flops on Trump, praising his 'strong speech'
ORLANDO, FLORIDA - FEBRUARY 26: Rep. Madison Cawthorn (R-NC) addresses the Conservative Political Action Conference being held in the Hyatt Regency on February 26, 2021 in Orlando, Florida. Begun in 1974, CPAC brings together conservative organizations, activists, and world leaders to discuss issues important to them. (Photo by Joe Raedle/Getty Images)
PHOTO: Joe Raedle/Getty Images
ORLANDO, FLORIDA - FEBRUARY 26: Rep. Madison Cawthorn (R-NC) addresses the Conservative Political Action Conference being held in the Hyatt Regency on February 26, 2021 in Orlando, Florida. Begun in 1974, CPAC brings together conservative organizations, activists, and world leaders to discuss issues important to them. (Photo by Joe Raedle/Getty Images)
Now playing
04:12
Women allege sexual misconduct against North Carolina GOP lawmaker
trump investigators murray dnt 03012021
PHOTO: CNN
trump investigators murray dnt 03012021
Now playing
02:56
Five elected investigators are turning their attention to Trump
Now playing
03:12
Avlon on CPAC: It was a hyperpartisan temper tantrum
New York Gov. Andrew Cuomo speaks during a news conference at a COVID-19 vaccination site in the Brooklyn borough of New York, Monday, Feb. 22, 2021. (AP Photo/Seth Wenig, Pool)
PHOTO: Seth Wenig/Pool/AP
New York Gov. Andrew Cuomo speaks during a news conference at a COVID-19 vaccination site in the Brooklyn borough of New York, Monday, Feb. 22, 2021. (AP Photo/Seth Wenig, Pool)
Now playing
02:26
Haberman: This is the first time I can remember Cuomo apologizing
Now playing
02:11
'Sad': Kinzinger blasts Hawley's CPAC remarks
New York Gov. Andrew Cuomo speaks during a news conference at a COVID-19 vaccination site in the Brooklyn borough of New York, Monday, Feb. 22, 2021. (AP Photo/Seth Wenig, Pool)
PHOTO: Seth Wenig/Pool/AP
New York Gov. Andrew Cuomo speaks during a news conference at a COVID-19 vaccination site in the Brooklyn borough of New York, Monday, Feb. 22, 2021. (AP Photo/Seth Wenig, Pool)
Now playing
01:12
Gov. Andrew Cuomo responds to allegations of sexual harassment
(CNN) —  

Senate Republicans aren’t ready to embrace the White House’s proposal to overhaul the nation’s legal immigration system, amid skepticism about elements of the plan and the timing of it.

At a closed-door lunch Wednesday, Trump’s son-in-law and senior adviser Jared Kushner, who spearheaded the proposal, faced questions from GOP senators about the range of immigration matters that are left out of his plan, with some arguing that the plan needs to address other matters in order to get broader support.

Kushner’s argument: Focus on issues that could get broader support. But Republicans argue that it’s simply not feasible since diving into immigration opens up a range of hot-button issues that have long divided Congress, namely what to do about illegal immigration, and those are inevitably going to reemerge.

“We all know what those are,” said Republican Sen. Mike Braun of Indiana, who supports increasing legal immigration. “He said they aren’t going to disregard those. He said we are going to focus on this because this ought to be something we all can agree to. Why would the Democrats not be for more legal immigration with the focus on who we are bringing in?”

Others made clear that they need to review the details.

“I’m not on the bill yet,” said Sen. Rob Portman, an Ohio Republican, who noted the measure doesn’t include anything for undocumented immigrants already in the US. “I’m for border security and moving toward merit based system. … I just need to look at the specifics.”

Kushner has pushed to get all 53 GOP senators on board, but some Republicans privately acknowledge there’s little chance that will happen – and doing so seems to be a waste of energy since it has little chance of becoming law.

In May, President Donald Trump announced a broad immigration plan that would replace long-standing, family-based immigration rules with a points-based system, otherwise known as a merit-based immigration system. Kushner spent months prior to its unveiling meeting with a number of immigration and business groups.

But any measure revamping the nation’s immigration system would need to pass through Congress – a heavy lift, particularly with a Democratically-controlled House and Republican majority in the Senate.

Sen. Ron Johnson, a Republican from Wisconsin who chairs the Homeland Security Committee, said he supports Kushner’s plan. He said Kushner is smart to try to pass individual solutions to the immigration problem because Congress has proven it can’t pass a comprehensive bill. But he acknowledged many of his GOP colleagues don’t support that approach.

“He is focusing on a limited part of the problem. Most members realize that in order to pass something, you’re going to need to expand the universe of what needs to be dealt with,” Johnson said.

For instance, Florida Republican Sen. Rick Scott said he’d like to see a fix for recipients of the Deferred Action for Childhood Arrivals program added to the bill.

“I’m very supportive of DACA – we have a lot in my state,” he said. “So I think whatever we do, it’s important we include them.”

Sen. Kevin Cramer, a Republican from North Dakota, said that Kushner’s presentation didn’t have any new details in it and that it was really just a broad overview of their effort. Cramer said that he wasn’t exactly sure why Kushner came at his particular moment. He said he thought Kushner was looking at “building enough support.”

“There is probably some sort of critical mass they have in mind,” he said.

Pressed on why he sounded so unenthusiastic, Cramer said, “I like it. I like what they are doing especially on the high-skilled worker side of things, but I don’t think any of us are overly optimistic that something would actually pass and so maybe there isn’t the timing urgency there would be if we were up against some sort of deadline.”

Asked why Kushner came Wednesday, Cramer said he wondered that himself.

“I was sort of curious about that. It was great to see him. I like Jared a lot, but actually that thought crossed my mind. I wonder if he wanted to come update us or Mike didn’t have a program for today,” he said, referring to Sen. Mike Lee of Utah, who is responsible for planning the steering lunch every Wednesday.