He said any deal on the Deferred Action for Childhood Arrivals program would require Democratic support because Republicans don't have to votes to pass legislation otherwise. DACA, which gives protections to young undocumented immigrants brought to the United States as children, expires in the spring.
"For many years ... they've been talking immigration and never got anything done," Trump told reporters after the swearing-in of new Health and Human Services Secretary Alex Azar. "But hopefully the Democrats will join us, or enough of them will join us, so we can really do something great for DACA and for immigration, generally."
A senior White House official told reporters last week that Trump plans to use the annual speech as a sales pitch for immigration, which likely would include funding for a wall along the United States' border with Mexico.
Tuesday will be Trump's first official State of the Union address, though he did address a joint session of Congress in March. The president said Monday he's worked hard on what he describes as "a big speech -- an important speech" that also will touch on "our great success with the markets and with the tax cut."
"It's going to be, I think, a very important speech on trade," Trump said. "The world has taken advantage of us on trade for many years. ... We're stopping it cold. And we have to have reciprocal trade. It's not a one-way deal anymore."
Senior administration officials said viewers also should expect Trump to offer more details about his proposed $1 trillion infrastructure plan. Speaking to the Conference of Mayors last week in Washington, Trump said the investment "will actually, probably, end up being about $1.7 trillion."
Trump on Wednesday said he'd talk about infrastructure during Tuesday's speech, but would put out the full details "in a week or two."
An official said that overall, Trump's speech will push the theme of unity.
"The speech will make clear all groups are benefitting under this presidency," the official said. "The president is going to show that all income groups, all people from all backgrounds are being lifted up by his policies."
Jennifer Grossman, former speechwriter for President George H.W. Bush, said that because Trump frequently talks directly to the public via Twitter, his State of the Union speech likely won't matter as much as previous presidents' did.
"It will be evaporating as quickly as morning dew," she told NPR. "I don't think his base will be watching or listening to the speech. They will be following his Twitter feed, whatever he says the speech was about."
Grossman said the "pageantry" of the speech would be worth noting.
"It's not just what the president says. It's not just how he delivers it. It's how he walks into the room, how people interact with him," she said.
Part of that pageantry is who Trump chooses to bring as guests to the event. The White House announced several guests for the president and first lady Melania Trump, including three who were involved in rescue and recovery efforts associated with natural disasters in 2017.
Others include injured veterans, people impacted by gang violence and drugs, and those who stand to benefit from the Republican tax overhaul.
"Some of these individual stories are heroic. Some are patriotic. Others are tragic," White House press secretary Sarah Sanders said during Monday's press briefing. "But all of them represent the unbreakable American spirit and will inspire our nation to continue growing stronger, prouder and more prosperous."
And it's not just the president who will bring guests to the State of the Union. Dozens of congressional Democrats are expected to bring so-called Dreamers -- recipients of DACA protections -- as guests in support of renewing the program for up to 1.8 million undocumented immigrants. At least 10 members of Congress have said they'll bring victims of sexual assault or women activists in support of the #MeToo movement.
Others, though, have said they won't attend the speech.
Rep. John Lewis, D-Ga., said he's boycotting over Trump's comments about immigrants from African nations and Haiti; Rep. Jan Schakowsky, D-Ill., said she won't attend because of Trump's "racist" behavior; and Supreme Court Justice Ruth Bader Ginsburg, who went to all of President Barack Obama's speeches, won't attend, along with justices Clarence Thomas and Samuel Alito, who usually skip the event.