He also tweeted, "What are Democrats afraid of Americans hearing?"
During the 19th Century and up until the presidency of Woodrow Wilson, these annual State of the Union messages were delivered to Congress in writing.
There was no immediate response from the White House.
Pelosi left unclear what would happen if Trump insisted on coming despite the welcome mat being pulled away.
We know Trump himself is the king of saying absolutely nothing with lot of words and a few choice lies, but it appears that ability has trickled down to his administration-perhaps the only time trickle-down has ever actually worked.
Trump stayed quiet on the request throughout the day. John Thune of South Dakota, the No. 2 Senate Republican.
The White House invited rank-and-file lawmakers to lunch with Trump at the White House as part of a strategy to build support from centrist Democrats and newly elected freshmen, including those from areas where the president is popular with voters.
Trump wrote a letter to Pelosi on Thursday informing her that her trip had been postponed and would be rescheduled after the shutdown. The previous record was a 21-day shutdown in 1995, when Gingrich was House speaker and Bill Clinton was President and Clinton and the Republican Congress clashed over the federal budget.
Trump on Wednesday is expected to sign legislation that would ensure 800,000 federal employees will receive back pay when the government reopens. That was the practice in the past.
While the Constitution requires the president deliver a State of the Union address, there's no language in there that demands it be a speech or in person. In the letter, she lied about the Secret Service being incapable to provide adequate security for the event. Last week, he said in an interview on PBS' "NewsHour" that furloughed federal workers who are not getting paid during the shutdown are "better off" because they didn't have to use vacation days around the holidays.
Minnesota Democratic Rep. Dean Phillips said Wednesday that the fact that lawmakers of both parties were sitting down and talking with Trump was progress in itself.
Pelosi reiterated she is willing to negotiate money for border security once the government is reopened, but she said Democrats remain opposed to Trump's long-promised wall.
Graham, who is close to Trump, has been among the most outspoken Republican advocates of temporarily halting the shutdown.
Afterward, White House Press Secretary Sarah Sanders called the meeting "constructive". Trump and others on-and-off used the term "wall".
Rep. Jim Himes of CT, another centrist Democrat, said the White House is "grasping at straws".
Many Republicans were unwilling to sign on to a letter led by Graham and Sen.
Still, even those in the White House who were skeptical that Democrats would show up saw a strategic advantage to inviting them: their lack of participation could give Trump ammunition to make the case that he's trying to solve the crisis, while Democrats are refusing to sit down at the negotiating table. "We commit to working to advance legislation that can pass the Senate with substantial bipartisan support", the senators said in their own letter to the president. They are people on every side of this border debate.
The Washington Post reported that Food and Drug Administration workers also have been called to work without pay during the shutdown.
The House and Senate announced they are canceling next week's planned recess if the shutdown continues, which seemed likely.