EXCLUSIVE: Top Republican senators, led by Sen. Lindsey Graham, R-S.C., plan to meet Thursday at the White House with President Trump to discuss possible immigration measures in case the Supreme Court strikes down an Obama-era ruling shielding illegal immigrants from deportation, Fox News has learned -- a push likely to revive concerns among Trump’s base of an election-year “amnesty” push.

The lawmakers are set to meet, at the invitation of the White House, with Trump around noon to discuss what would happen should the top court strike down the Deferred Action for Childhood Arrivals (DACA) executive order, a source familiar with the negotiations said. A decision on DACA is expected in June. The Republicans are said to include Sens. Ted Cruz, R-Texas; Kevin Cramer, R-N.D.; Tom Cotton, R-Ark.; Martha McSally, R-Ariz.; Mike Lee, R-Utah; Ron Johnson, R-Wis.; Thom Tillis, R-N.C. and David Perdue, R-Ga.

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Graham, on Thursday morning, told Fox News that the meeting was going ahead and it was related to the coming DACA ruling.

"Just to see, you know, where we are in terms of the DACA Supreme Court case, [there's a] pretty good chance that the president will win, being able to set aside the Obama-era DACA regulations and what's the play after that," he said.

The source told Fox News that a comprehensive immigration reform deal was to be discussed, but a Graham spokesman pushed back, saying that the meeting is to discuss DACA, and comprehensive immigration reform was just one of a broad range of topics that could potentially be discussed.

A spokesman for Lee confirmed to Fox News that the senator had been invited to the White House to talk immigration, but that he hadn't heard anything about a deal for Dreamers. The offices of Sens. Johnson and Cramer also confirmed their attendance at the meeting.

Trump vowed during his 2016 campaign to end DACA but has also said he is open to a broader bill that would allow those affected -- young migrants dubbed “Dreamers” who were brought to the U.S. illegally as children -- to stay as part of broader immigration plan that sees funding for border security in exchange for a "pathway to citizenship" as well as expansion of visas and green cards. Even as Republicans fight DACA in court, there is some bipartisan appetite for finding a legislative way to protect Dreamers, considering that in many cases the decision to illegally enter the U.S. was not their own.

An eventual, if elusive, immigration pact, particularly one that succeeds by picking up Democratic support, could essentially boost the president’s image among moderates as a “deal-maker” who can get things done where others have failed. Yet, it is risky and likely to fuel further concern among immigration hawks in Trump’s base.

"It is risky, it makes sense that Graham is the one taking the lead given his prominent role in past efforts...but it would make a lot more sense if someone hawkish took the lead on this," Mark Krikorian of the Center for Immigration Studies, which advocates for lower levels of immigration, told Fox News.

Krikorian said that Trump risks being seen as "selling out" on his signature campaign promises on immigration, but the White House could deal with that risk by coming up with a deal the president can defend, and including provisions that no-one beyond the actual DACA recipients, such as their relatives, gets legal status as well.

"A tough enough deal that he could justify it, because there is political support for legalizing people who lived here for years and came here as 8-year-olds," he said.

While the delegation includes a range of immigration hardliners whose involvement could potentially dilute anything too far-reaching, Graham has been eyed with suspicion by conservative activists for years for his pushes on immigration reform.

Conservative radio host Rush Limbaugh once dubbed the South Carolina senator “Lindsey Grahamnesty” for his repeated efforts, alongside then-Arizona Sen. John McCain, to try and get immigration reform through Congress -- a move that was killed during the Bush administration after a push by conservative activists. In 2018, conservative commentator Ann Coulter called Graham the "single worst person to negotiate" such a deal.

Pushes for immigration reform have also been blamed for helping doom the presidential aspirations of a number of top Republicans, including Jeb Bush, Sen. Marco Rubio, R-Fla., and even Graham himself.

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A call for a comprehensive immigration reform plan was included in a post-2012 election "autopsy" report by the Republican National Committee. The nomination of Trump in 2016 was seen as a rebuke to that call, particularly by the party base.

"What Lindsey Graham is trying to do isn't only bad policy, it's bad politics. His amnesty agenda is in line with the 2012 GOP autopsy report that should have been dead and buried after President Trump was elected," the source familiar with negotiations told Fox News.

Graham himself has at times taken a tough stance on illegal immigration. Last year, he introduced a bill that would end asylum claims at the border and return unaccompanied minors to their home countries, as part of an effort to end the then-escalating crisis at the border.

Trump has racked up a series of wins at the border, securing funding for the wall, and dramatically reducing border crossings by implementing international agreements with neighboring countries. But there remains in some pro-Trump circles a sneaking suspicion that a betrayal on so-called amnesty for illegal immigrants is just around the corner, considering the hefty appetite in Washington D.C. for a deal.

While it’s not immediately clear what the deal could include, there are a number of bills and proposals already circling that could be covered -- in measures both passed by the House or mentioned in prior stabs at immigration reform.

Krikorian said he believes there will likely be enforcement measures in any agreement, but said there should also be an offsetting reduction in legal immigration if DACA-recipients are going to end up with legal status.

"If we're giving away 700,000 green cards, that's almost an extra year of immigration, there needs to be some reduction," he said.

The Democrat-controlled House passed a farm bill in December that granted a pathway to citizenship for illegal immigrants working in the agriculture industry. While it hasn’t yet been taken up by the Senate, it could be brought in to discussions. Other aspects, including green card reform, legal status for DACA recipients and visa reforms, could also be part of the deal, the source said.

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Trump too has tried to push a DACA deal before, in January 2019 offering Democrats legal status for DACA recipients in exchange for money for the border wall. He later backed away from the deal after pushback from immigration hawks.

Politico reported last month that a White House proposal was in the works to overhaul America's immigration system to replace it with a merit-based system. But that too has struggled with hawks, as it doesn't make the E-Verify work verification system mandatory, nor does it reduce overall immigration levels.

Fox News' Jason Donner contributed to this report.