Washington (CNN) President Donald Trump is impatient to return to the immigration negotiating table, despite advice from some aides that he allow lawmakers to strike their own agreement, people who have spoken with him said.

Peeved by the perception the government funding stalemate was resolved in spite of -- and not owing to -- his leadership , Trump is eager to rebut the notion he sat on the back benches during the debate over ending the shutdown, the people who have spoken with him said. Even before the government reopened, the rush to Trump's ear began in earnest Monday as a half-dozen of the Senate's immigration hard-liners came to the White House for talks. He held a separate meeting with two moderate Democratic senators.

A year into his administration, Trump's positions on immigration remain muddled, despite insistence from the White House that he has clearly outlined his views. A series of failed deals over the past several weeks underscored his shifting positions.

While the White House rushed to declare political victory as the impasse ended, the fact that the President may have been more helpful staying on the sidelines than being deeply engaged raised serious questions about his role going forward.

Simply a bystander?

The President wasn't seen in public on Monday for a third straight day.

He spent much of his time in the White House residence, closely following television coverage of the government shutdown, while making occasional calls to Republican lawmakers and his advisers. He spent far more time focused on the public relations fight than the legislative one.

"What the President did clearly worked," White House press secretary Sarah Sanders said Monday when asked whether Trump was simply a bystander.

The three-day government shutdown shined a fresh light not only on the dysfunction of Washington, but also on the President's vacillating views. While he declared "I'll take the heat" less than two weeks ago during a bipartisan meeting on immigration, Trump was all but absent when that heat actually came.

Sen. John Thune of South Dakota, chairman of the Republican conference, said Trump needed to be a central player in order for the immigration debate to succeed in the House.

"It's going to take a tremendous amount of input, support and encouragement from the President," Thune told CNN on Monday. "He is going to be key to any solution going forward. His role will be an important one. I expect we will be hearing from him early and often once these discussions get underway."

Yet there is little to suggest the underlying dynamics, which led to the shutdown, have changed.

Trump has yet to clearly articulate what must be included in a deal to extend legal status to so-called Dreamers. He retains only a loose grasp on the details and nuance of immigration policy. And the White House aides who have operated behind-the-scenes to repeatedly scuttle agreements despite Trump's receptiveness remain central players.

That includes chief of staff John Kelly, who twice intervened when it appeared Trump was warming to moderate immigration deals, and Stephen Miller, the senior policy adviser who has repeatedly encouraged a harder line in negotiations.

Miller in particular has come under criticism from some lawmakers, who have cast him as an overly conservative voice that is preventing progress. Over the weekend, Sen. Lindsey Graham of Carolina alleged Miller and other aides are pulling the strings and reining in the president. A Republican familiar with Graham's thinking believes he is trying to directly communicate with Trump, knowing that one thing above all irks him: Any suggestion that he's not in charge. Trump and Graham have not spoken directly, a White House official said.

Miller and Kelly, along with Homeland Security Secretary Kirstjen Nielsen, participated in Trump's meeting Monday with Senate immigration hard-liners and the pair of top aides were also present in the meeting with Democrats.

Better off on the sidelines

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As Trump watched the weekend machinations over reopening the government from his third-floor perch at the White House, he repeatedly told aides that he wanted to be more involved in discussions. They told him he'd be better off on the sidelines, encouraging lawmakers to come to an agreement themselves. And so he spent Saturday and Sunday watching television coverage and phoning friends to hear their advice.

"He's anxious to get back into the topic and reach a solution," said Sen. John Cornyn of Texas, the No. 2 Republican, who was among the lawmakers who met with Trump on Monday.

To some GOP lawmakers, Trump becoming more involved amounts to a positive step.

"What's been difficult in dealing with the White House is not knowing where the President is. That is what was holding us back," said Sen. Jeff Flake, the Arizona Republican frequently at odds with the White House. "I don't think it will change. I hope that it does. I hope the President will say, here's what we need and here's what we'll stick with."

Short of a full-throated endorsement on a plan to extend legal status to so-called Dreamers, any legislation faces a highly uncertain future in the House. The immigration debate has become far more divisive than the last one five years ago, when a comprehensive deal passed the Senate but was never called for a vote in the House.

A critical decision faces Trump for how he engages in that debate. The entire episode could repeat itself in only three weeks.

"Presumptively we'll be back in the same situation a couple of weeks from now. We want to deal with the DACA issue, the Dreamer issue, but I don't think we are any closer to having an agreement on that," said Alex Conant, a Republican strategist who worked on the last immigration debate. "I think it's highly likely the government may shut down in three weeks over the same issue."