President Trump gives a thumbs-up as he walks from Marine One upon arrival Sunday on the South Lawn of the White House, after spending the weekend at Camp David, the presidential retreat in Maryland. (Saul Loeb/AFP/Getty Images)

President Trump expressed misgivings about his administration's infrastructure plan Friday at Camp David, telling Republican leaders that building projects through public-private partnerships is unlikely to work — and that it may be better for the government to pursue a different path.

Then on Saturday morning, Gary Cohn, the president's chief economic adviser, delivered a detailed proposal on infrastructure and public-private partnerships that seemed to contradict the president. He said the administration hoped $200 billion in new federal government spending would trigger almost $1 trillion in private spending and local and state spending, according to people familiar with his comments. Cohn seemed to present the plan as the administration's approach, although the president had suggested such an approach might not work. 

The seemingly contradictory statements, made within 24 hours of each other, show the uncertainty of the administration's approach to its top legislative priority in 2018: building roads, bridges and highways. Trump and his White House have been determined to pitch an infrastructure plan in 2018, despite Republican misgivings about the cost, a rapidly rising deficit and a preference to consider other matters first. 

White House officials and Hill aides confirmed the president's comments. Another White House official briefed on the comments said that Trump was musing aloud and that the administration still planned to pursue public-private partnerships for infrastructure. This person, though, said Trump had continually expressed skepticism behind the scenes about such a plan.

"He doesn't think they will work," this person said.

Trump and Cohn have had a rocky relationship after the economic adviser criticized the president's comments about white-supremacist riots in Charlottesville, suggesting that there were "many fine people on both sides." Several White House advisers have said recently that the former Goldman Sachs banker may exit. Asked about that Saturday, Trump pulled Cohn up to a news conference stage and asked if he was staying. The economic adviser said yes and that he was having fun.

"Gary, hopefully, will be staying for a long time," Trump said. "Now, if he leaves, I'm going to say: 'I'm very happy that he left.' Okay? All right?"

"I'm happy," Cohn said.

In a statement Sunday night, deputy White House press secretary Lindsay Walters said: "The President's infrastructure vision is very clear and is based around 2 main goals: leveraging federal funds as efficiently as possible in order to generate over $1 trillion in infrastructure investment and expediting the burdensome and lengthy permitting process."

Republicans are loath to spend $1 trillion on infrastructure, as the deficit is expected to grow considerably after the tax plan passed in December. Trump did not specifically delineate how he would pay for the projects without the partnerships.

During the campaign, Trump promised a $1 trillion infrastructure plan that he said would create millions of jobs through a combination of investments from the federal government and private companies. Staff members at the White House have spent months assembling a package of ideas, though his first budget just allocated $20 billion a year over 10 years for the mostly unspecified projects.

In September, though, Trump began musing to Democrats and others that the public-private partnership idea might not work. He referenced at least once, for example, some projects in Indiana that he believed did not work out the way the private sector had promised. In 2014, then-Gov. Mike Pence arranged a deal with Isolux Corsan, a Spanish construction firm, to extend a stretch of interstate in the southern part of Indiana. The firm had turned in the lowest bid but never completed a project in the United States before, and it fell behind schedule. The state of Indiana had to eventually dissolve the partnership and issued public debt to finish the project, though it still remains incomplete.

Trump's repeated complaints about the effectiveness of public-private partnerships have infuriated and surprised some administration aides who have worked on the plans for months. They were hoping to propose a package of infrastructure goals later this month, though that timetable remains fluid.

Democrats have often said they would support more infrastructure spending, and many labor unions have also said they would like to work with Trump on these plans. But they have remained wary of how Trump would plan to pay for any of the projects, and those questions appear to remain unresolved.

 The weekend, White House and legislative leaders said, was largely marked by bonhomie — even if many key decisions on issues such as immigration, infrastructure and funding the government were not made. Trump had clashed with Senate Majority Leader Mitch McConnell (R-Ky.) earlier in his tenure and had been at times critical of House Speaker Paul D. Ryan. (R-Wis.). The intent of the weekend was to build camaraderie, officials said.

Trump vented about former White House strategist Stephen K. Bannon, to the pleasure of McConnell and others, and criticized a tell-all book on his administration from the author Michael Wolff, saying the author barely knew him and had made up large parts of the story.

Wolff spent considerable time in the West Wing and talked to Trump, although others have pointed out factual issues in the book.

There was little talk about repealing and replacing the Affordable Care Act or launching a campaign to curb entitlement spending — issues that are now unlikely to come up legislatively in 2018.

Trump had previously said he wanted to return to health care early in 2018, but he has instead told advisers in recent weeks that he can sell repealing the individual mandate. Top officials have also convinced him that there is no path to repealing the law. 

Trump has also decided that pursuing cuts to the country's entitlement spending in 2018 is not a good bid for him, and he purposefully left it out of public comments, advisers said.

White House officials complained that their nominees weren't going through the Senate quickly enough — much of the government is unfilled — and pushed McConnell to do more, people briefed on the summit said. The White House has been criticized for its slow pace of nominating people to key jobs.

Homeland Security Secretary Kirstjen Nielsen briefed legislators on what the administration wanted on border security in exchange for a deal on the Deferred Action for Childhood Arrivals program, and there was a consensus that it needed to happen before March, when a deadline set by the White House expires.

Trump told the leaders that they needed to focus on selling their 2017 accomplishments and continued to cast his administration in historic terms, even in private. The president has the lowest poll numbers of a first-year president in decades, and leading Republicans fear privately that the midterm elections could be damaging. 

Damian Paletta contributed to this report.