Senate Minority Leader Chuck Schumer said President Trump and Democrats agreed to spend $2 trillion on infrastructure over 25 years in a "constructive" White House meeting, and will meet again in three weeks on how to pay for it.

"We agreed on a number, which was very very good, $2 trillion for infrastructure," Schumer told reporters outside the White House Tuesday. "Originally we had started a little lower, even the president was willing to push it up to $2 trillion. And that is a very good thing."

But that number, reached in a meeting with only Democratic members present and no Republican members present, could be in jeopardy if Republicans lack the appetite for agreeing to spend that much.

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Schumer and Pelosi said the roughly 90-minute meeting emphasized the importance of building up broadband, bridges and highways. They insisted Congress and the White House can work together at the same time as Congress is exercising oversight in Congress. Mr. Trump has expressed doubt about legislation and investigations happening simultaneously.

"In previous meetings, the president has said, 'if these investigations continue I can't work with you.' He didn't bring it up," Schumer said. "And so we're going, I believe, we can do both at once. We can come up with some good ideas on infrastructure, we want to hear his ideas on funding, that's going to be the crucial point in my opinion. And the House and the Senate can proceed in its oversight responsibilities. The two are not mutually exclusive, and we were glad we didn't make it that way."

The White House's official read on the meeting was positive, too. White House Press Secretary Sarah Sanders said Mr. Trump and Democrats "had an excellent and productive meeting on rebuilding our nation's crumbling infrastructure including roads, highways, bridges, tunnels and railroads, modernizing our air travel system, and expanding broadband access for our great farmers and rural America."

"The United States has not come even close to properly investing in infrastructure for many years, foolishly prioritizing the interests of other countries over our own," Sanders said in a statement. "We have to invest in this country's future and bring our infrastructure to a level better than it has ever been before. We will have another meeting in three weeks to discuss specific proposals and financing methods."

A Democratic aide confirmed there was "not a single mention" of oversight, subpoenas or investigations in the meeting, and Mr. Trump even shared some white Tic-Tacs with the speaker, which he has done before.

One Democratic source said that at one point during the meeting, Pelosi tried to break up a side conversation between Mr. Trump and Schumer by saying, "If I may have your attention ... Mr. President ... Chuck ... Kids."

The White House didn't have a blueprint going into the meeting with Democrats and other top administration officials, including Transportation Secretary Elaine Chao. Democrats set out a handful of key — albeit general — principles for piecing together an infrastructure deal. Schumer and Pelosi wrote to Mr. Trump this week, listing three pillars of any infrastructure proposal: significant, new federal funding; clean energy to address climate change; and it must be able to be carried out by many businesses owned by women, veterans and minorities.

"We're feeling our way, we don't have anything in concrete," top Trump economic adviser Larry Kudlow told reporters outside the White House Monday. "We are developing our own policies internally. We very much want to hear what the Senate and House members, what the Democrats want to say, and we will try to react to that."

Last year, the White House put forward an infrastructure proposal that was criticized for providing very little federal funding and relying heavily on the private sector and private-public partnerships.

Mr. Trump has long expressed hope that infrastructure is one topic on which the White House and top Democrats can work together. When Democrats reclaimed the House in November, Mr. Trump said he thought infrastructure was one key issue they could work on together.

"Now we have a much easier path because the Democrats will come to us with a plan for infrastructure, a plan for health care, a plan for whatever they're looking at, and we'll negotiate," Mr. Trump said in a press conference on Nov. 7, 2018. He added, "From a dealmaking standpoint, we are all much better off the way it turned out" than if Republicans had kept control of the House."

But infrastructure won't be easy. Just take it from a former administration official who was involved in discussions over last year's proposal, a proposal that was never actualized.

In the 2018 infrastructure push, the former official said the president was "very involved" involved in discussions, and was "quite open" to a gas tax. But a gas tax never made it into the proposal, and would likely meet GOP opposition. Rep. Kevin McCarthy, now the House minority leader, supported an initiative to repeal the gas tax in California, and the former official said it's hard to imagine McCarthy would be supportive of bringing any bill including a gas tax to the floor this time around.

The source said they knew last year's infrastructure proposal was not going to come to fruition when then-chief White House economist Gary Cohn left the administration. The former official called Cohn a "force of nature" and "phenomenally effective."

But the bottom line is the president "wants to negotiate, he absolutely would love to sit down and hammer out a deal," the former official said. Mr. Trump wants to "fix the problem" and have "the world's best infrastructure in the U.S."

"He has experience in the area, right, he's actually built things before and so he feels very comfortable in the issue area. And he wants a deal. Right? But he wants a good deal."

In the former official's point of view, one big obvious roadblock last time around, which will also pose a challenge this time around, is that "at the end of the day," someone has to pay for it. The federal government, in this former official's perspective, doesn't have nearly as much unilateral control of infrastructure as it once did. The administration's 2018 infrastructure proposal was heavily criticized for relying heavily on state and local governments, and providing little additional federal aid. The former official said the problems with U.S. infrastructure run "much deeper" than a lack of revenue, but that message might not translate for Democrats.

"Just throwing more money into the same old buckets does not solve this problem," the former official said.

Climate change, which the Democrats mentioned in their letter to the president outlining their priorities, is sure to be a contentious point when it comes up for discussion this time around as well, the former official noted.

"Yeah it's going to immensely challenging, right. I mean infrastructure ... it's somewhat counterintuitive and you need to think about it. And do we need a new system? I think everyone agrees yes we do, what's the new system look like, there's not agreement on that, so that's hard. On top of that you can say, 'Oh, and we want to address climate change.' So, is that Green New Deal climate change?...What does that mean and how big does that get? I think it's going to be very hard for Speaker Pelosi to have a climate change conversation on infrastructure that doesn't also touch on the Green New Deal."

— CBS News' Rebecca Kaplan, Fin Gomez and Paula Reid contributed to this report.