Washington (CNN) The escalating immigration drama is crystallizing for some lawmakers and presidential advisers their long-held views of John Kelly, President Donald Trump's chief of staff: He's a fierce advocate for hardline policies that drastically limit the number of people entering the US. And he'll remain so, even as the government barrels toward a potential shutdown over the issue.

"Kelly is a hardass," said one Republican lawmaker, who requested anonymity to discuss Kelly's approach to immigration. "Some people might think he's softer; he's a hardass, also. And a straight, straight shooter. He doesn't sugar coat things."

Kelly has been seen as a stabilizing force on an erratic presidency, taming an unorganized White House. He appealed to Democrats Wednesday by calling Trump "uninformed" on some immigration issues, according to a source familiar with the comments.

But such moves don't change the fact that the administration, with Kelly's full support, will continue to aggressively enforce immigration laws, according to a senior government official. And Kelly is the person who helped sink a bipartisan immigration deal that emerged last week.

The White house chief of staff warned Trump the agreement would incite anger among his base, who expect him to deliver on his promises to build a border wall and deport undocumented immigrants, according to two White House officials and a congressional source familiar with the situation. And he sent word to Capitol Hill, where like-minded Republican lawmakers were summoned with minutes to spare to attend a White House sit-down with the crafters of the deal, who later claimed they were blindsided by the move.

Kelly's tactics, which culminated in a heated, profanity-laced Oval Office meeting, disappointed some lawmakers and administration aides, who have privately expressed fears that his hardline views are obscuring chances for an immigration deal. And it opened him to criticism from some lawmakers, who began publicly saying this week that Trump isn't well served by his staff.

Full scope of voices

Kelly's supporters say he is merely ensuring the President is hearing from a full scope of voices as he weighs various proposals on an issue that was central to his rollicking presidential campaign. And the White House has publicly downplayed Kelly's role in orchestrating last Thursday's meeting, which devolved into Trump deriding some countries as "shitholes" or "shithouses," depending on the telling.

Instead, the White House has insisted that it was Trump's decision to invite Republicans to the session in the hopes of hearing their views on the emerging plan.

Speaking Wednesday, Kelly said the bipartisan agreement offered by Republican Sen. Lindsay Graham and Democratic Sen. Dick Durbin didn't meet Trump's criteria

"That deal that came over was supposed to be two things: bipartisan and both sides of the Hill," Kelly told reporters on Capitol Hill in between meetings. "There were a number of other senators that had been involved in this from the beginning ... that were not consulted."

"The President has said from the beginning, it's got to be bipartisan and unless it involves the House as well as the Senate, it's going to go down again as a bill that does not pass into law," he said.

Kelly met for an hour Wednesday with members of the Congressional Hispanic Caucus and listened to concerns about how the administration has approached immigration. The meeting was "cordial" and "positive," participants said, but didn't produce any new path toward an agreement. While lawmakers made a point to say they appreciated the session, they expressed disappointment that Kelly had not come armed with any proposals to negotiate and that he didn't seem well-versed in the bipartisan proposals under development in Congress.

Among the concerns aired in the meeting were the administration's use of the term "chain migration" to describe the process of citizens and green card holders bringing their extended family to the US.

"Please don't use that term," Rep. Linda Sanchez, D-California, told Kelly, explaining the phrase is considered loaded and offensive. Kelly didn't apologize, but acknowledged the term is disputed, according to a source in the room.

Spearheading immigration talks

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As the immigration debate has heated up, Trump tasked Kelly with spearheading talks on the issue in the hopes of striking a deal that would adhere to his campaign promises. He's taken more of a personal role in meetings with aides and lawmakers, where his deeply held views have been apparent, according to people who have participated in them. That has led to some grumbling from other administration officials, who believe Kelly's hardline stance on immigration has obfuscated opposing views.

As secretary of Homeland Security, Kelly gained the President's approval by channeling the unwavering immigration stance that Trump espoused on the campaign trail, despite offering what appeared to be a more moderate stance during his confirmation hearing a year ago -- including downplaying the importance of a border wall.

His ardent approach -- paired with a no-nonsense Boston accent and a Marine's rigor -- is what led Trump to name him chief of staff, people familiar with Trump's thinking say.

His mandate entering the West Wing was to instill order among warring factions of aides and streamline the flow of information to the President. Outsiders also viewed him as a potentially moderating force on a President whose brash outbursts and appeals to nationalist sentiments had alienated some voters and establishment politicians.

But Kelly has sought to manage expectations, and has bolstered Trump during some of his most controversial moments, including backing up his views on Confederate monuments and appearing in the White House briefing room to defend Trump's phone call with the grieving widow of a slain US serviceman.

Toughest job

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Kelly has told friends his role as Trump's top aide has been the toughest job of his career, which has included deployments in Iraq and as commander of US Southern Command. But he's also described the chief of staff role as immensely rewarding.

On immigration, Kelly has been supported inside the West Wing by Stephen Miller, a senior policy adviser whose hardline views on immigration are well known. Miller has been a staunch and outspoken proponent of limiting immigration to the US, and is viewed as the White House's guiding voice on the matter -- to the chagrin of Democrats working to strike an agreement.

"It's hard to find any effort to kill immigration legislation that doesn't have Steve Miller's fingerprints on it," Durbin said on Tuesday. "He's been an outspoken foe of immigration reform and opponent to DACA and the Dreamers from the start."

Kelly is "more of an adult," one person familiar with the situation said, and Trump believes that with him in charge, there's a better chance of getting something done. Another person said Kelly respects Miller but is the clear person in charge.

While Kelly may foster more goodwill on Capitol Hill than Miller -- who gained notoriety as an outspoken and rabble-rousing congressional aide -- the chief of staff's actions over the past week have prompted some lawmakers to air their misgivings publicly.

"I don't think the President was well served by his staff," Graham said on Tuesday, adding later: "I think someone on his staff gave him really bad advice between 10 and 12 on Thursday."

Asked whether he pinned the blame on Kelly, who as chief of staff has demanded rigorous order in the West Wing, Graham demurred: "I think General Kelly is a fine man but he's also part of the staff."

On Wednesday, Kelly darted between meetings on Capitol Hill meant to restart immigration talks after last Thursday's profanity-laden meeting. Aside from the Hispanic lawmakers, he met with four moderate Republicans, followed by two leaders of the conservative House Freedom Caucus and then went to meet with the bipartisan congressional leaders who are attempting to negotiate a deal.

Asked as he departed whether he would take into account the diverse set of views he'd heard, Kelly answered affirmatively.

"Yeah, sure," he said.