In August 2015 during his presidential campaign, Mr Trump had made his expectations for the border explicitly clear, as he parried criticism from then-rival Jeb Bush, the former Florida governor.
That theory will be put the test this week when the new House majority led by Pelosi gavels into session with legislation to end the government shutdown.
House Democrats did not confer with Senate Republicans on the package, but it is expected to have some bipartisan support because it reflects earlier spending bills already hashed out between the parties and chambers.
The partial United States government shutdown will nearly certainly be handed off to a divided government to solve in the new year.
President Trump also called out lawmakers for claiming a wall is old technology and won't work for security, saying it does when properly built.
Trump on Saturday blamed Democrats "and their pathetic immigration policies" for "any deaths of children or others" in US custody at the border, a ramp-up in rhetoric over wall funding.
In one of his tweets, Trump rejected that account.
Right now, the political calculus for both sides remains murky. Finally, Sen. Lindsey Graham (R-S.C.) said on Sunday that the wall was nothing more than a "metaphor" for border security. "I'm just asking people to sit down and rearrange the deal that was offered before".
After a Sunday lunch with Trump at the White House, Sen.More news: Meghan Markle Hinted At Her Due Date On Christmas Day
There has been little direct contact between the sides during the stalemate, and Mr Trump did not ask Republicans, who hold a monopoly on power in Washington until January 3, to keep Congress in session.
Schumer immediately began approaching Democratic senators after the midterm election to hear their views on Trump's $5 billion demand for the wall, according to a person familiar with the talks but unauthorized to speak publicly.
Trump's outgoing chief of staff John Kelly, who has been largely uninvolved in the shutdown negotiations, said in an interview published Sunday that the wall Trump is hammering Democrats over is not actually a concrete wall and hasn't been since the early days of the administration.
Within hours, Trump pushed back on Kelly's comments, tweeting that an "all concrete Wall was NEVER ABANDONED, as has been reported by the media".
Jones said border security is "essential" and funding should be "found internally" if Mexico won't fork over money to help pay for it - something Trump has often promised would happen.
Trump has attacked Democrats repeatedly on Twitter.
And if the shutdown drags into the new Congress?
Pelosi has reportedly been holed up at the tony Fairmont Orchid Hotel in Kona, on Hawaii's big island, where room rates can run from around $500 to a staggering $5,000 per night - and Nancy Pelosi is not hurting for wealth, so it's unlikely she's been slumming it in the $500-per-night one bedroom suites.
The shutdown is forcing hundreds of thousands of federal workers and contractors to stay home or work without pay.
"Less hula, more moola" for the Department of Homeland Security, she said.
- The departments whose funding lapsed represent about a quarter of the $1.24 trillion in government discretionary spending for fiscal year 2019.