But no rank-and-file House Democrats took the president up on the offer. Trump's move was seen on Capitol Hill as an effort to split House Democrats and pressure House Speaker Nancy Pelosi to make concessions in her standoff with the president over funding his proposed border wall.
"The president has laid out what he thinks a good plan is," Rep. Rodney Davis, R-Iowa, told reporters outside the White House at the conclusion of the lunch. "He's put a deal on the table. The sheer fact that there were no Democrats here to even talk with us I think shows the lack of willingness to compromise."
The White House invitation came nearly a week after direct negotiations between the president and Democratic leaders broke down during a 14-minute-long White House meeting that ended abruptly when the president walked out of the room after Pelosi said Democrats would not agree to fund a border wall, demanding Trump reopen the government before talks on border security could continue.
Though no Democrats ultimately decided to go to Tuesday's lunch, Democratic leaders left it up to rank-and-file members to decide for themselves.
During a closed-door meeting with Democratic leadership Monday night, Pelosi even jokingly encouraged the encounter, according to an aide in the room.
“They can see what we’ve been dealing with. And they’ll want to make a citizen’s arrest,” Pelosi joked, according to the aide.
House Democratic Caucus Chair Hakeem Jeffries said no one was discouraged from going to the White House but said that members should consider whether the president’s invitation was a sincere opportunity for dialogue or a photo op.
“The question I think everyone can reasonably ask is, is he inviting people to 1600 Pennsylvania Avenue to really try to resolve this problem, or to create a photo-op so he can project a false sense of bipartisanship,” Jeffries said.
Some Democrats cited scheduling conflicts for their reason for not attending, including moderate Rep. Stephanie Murphy, D-Fla., a leader of the moderate House Democratic Blue Dog Coalition.
“I have attended meetings with the president at the White House before, but a scheduling conflict prevented me from accepting this invitation. However, I continue to believe the Senate should pass and the President should sign the bills reopening government that the House already passed," Murphy said in a statement.
One Democratic aide said it appeared the meeting was organized relatively last minute, with Democratic members beginning to receive invitations from the White House to attend the Tuesday meeting on Monday afternoon.
Another Democrat, Rep. Joe Cunningham of South Carolina, a conservative freshman whose district was carried by President Trump in 2016 and who attended the celebration for the Clemson University football team at the White House Monday night, told reporters he hadn't been invited.
"Early in his administration, I had a chance to speak with him personally in the White House, saying, 'You know, it's not a bad idea to reach out to some members of the other party, just to get to know them a bit and open lines of communication,'" Rep. Ron Kind, D-Wis., a moderate, told ABC News.
Since then, he's said he's had "zero" interaction with the White House.
"Even his leg[islative affiars] people at the White House, there's zero work, zero contact. I don't even know who they are, I don't even know who is assigned to me. That's how bad his operation is being run right now," he said.
Though Kind is open to talking to the White House in principle, he pondered the utility of engaging with the White House in the midst of the current impasse: "Given where he is in negotiations, what's the point? Because it doesn't sound like he's willing to give an inch on anything right now, he's dug in.”
While Trump continues to insist on funding for a southern border barrier as a condition for ending the partial government shutdown, Democrats remain unwilling to negotiate on the president’s demands for border security until the government is reopened.
While recent polls show most Americans believe the president and congressional Republicans shoulder the blame for the current partial shutdown, Rep. Jodey Arrington, R-Texas, told reporters at the White House to not expect Trump will be swayed and back down on his demand for a border wall.
"This is why this president was elected," Arrington said. "You're asking questions related to polls, this president isn't taking polls, this president has the pulse of this country. And he understands that the safety and security of the American people is his first job."
The House plans to vote this week on two measures to reopen the government, funding shuttered agencies at current levels through February.
The president on Monday rejected a proposition from his close congressional ally, South Carolina Republican Sen. Lindsey Graham that the president reopen the government for a short period of time to allow for further negotiations and to then declare a national emergency if talks fail.
“I'm not interested. I want to get it solved. I don't want to just delay it. I want to get it solved,” Trump told reporters Monday, rejecting Graham’s suggestion.