President Trump Donald John TrumpUS reimposes UN sanctions on Iran amid increasing tensions Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally MORE has recently expressed his willingness to reach a deal with Democratic lawmakers on recipients of the Deferred Action for Childhood Arrivals (DACA) program, but two key White House aides have argued that an agreement requires harsher immigration rules, The New York Times reported.

According to the report, chief of staff John Kelly John Francis KellyMORE and senior policy adviser Stephen Miller have pushed for a tougher immigration policy, as lawmakers continue negotiations over a bill to fund the government. DACA, an Obama-era program that shields certain immigrants brought to the U.S. illegally as children from deportation, was central to those talks, which did not result in an agreement to stop the government shutdown that now stretches into its third day.

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GOP Sen. Lindsey Graham Lindsey Olin GrahamMomentum growing among Republicans for Supreme Court vote before Election Day Video of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral Warning signs flash for Lindsey Graham in South Carolina MORE has criticized Miller throughout the negotiations, the Times noted, with the South Carolina lawmaker referring to the Trump aide as an “outlier.”

“His heart is right on this issue; I think he’s got a good understanding of what will sell, and every time we have a proposal, it is only yanked back by staff members,” Graham said Sunday, referring to Trump.

“As long as Stephen Miller is in charge of negotiating immigration, we are going nowhere. He’s been an outlier for years,” Graham added.

Republican strategist Alex Conant told the Times that there’s a “real sense that there’s a disconnect between the president and his staff on immigration issues, and people on all sides are seeking to exploit that disconnect.”

“This is what happens when you have a president who is not clear and consistent on what he will accept: It emboldens all parties to take positions that they won’t compromise,” added Conant, who served as the communications director for Sen. Marco Rubio Marco Antonio RubioSunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Florida senators pushing to keep Daylight Savings Time during pandemic Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll MORE (R-Fla.) during his 2016 presidential campaign.

Center for Immigration Studies executive director Mark Krikorian also told the Times that the president “seems to make commitments that he is not going to keep.”

“His inclinations are hawkish on immigration, but he seems to like to be agreeable to people and nod his head when he’s at a meeting and people are saying things, and try to make a deal,” Krikorian told the newspaper.

Trump has also previously said that his proposed wall on the U.S.-Mexico border "must be part of any DACA approval."

Updated at 8:07 a.m.