Mr. Trump, meanwhile, has teased his address as a place to declare a national emergency, something that his own aides and Republican lawmakers have warned him against, and where he might also announce the details of a second summit meeting with the North Korean leader, Kim Jong-un. In an interview on Sunday, Mr. Trump said he would not reveal the details of that meeting, but noted, “You’ll be finding out probably State of the Union or shortly before.”

Last year’s address was punctuated by the death of Otto Warmbier, the American student who was killed in North Korean custody. At the time, Mr. Trump gave a saber-rattling address condemning the brutality of the North Korean government, and saluting Mr. Warmbier’s parents, who were his guests. Since then, however, Mr. Trump has sought common cause with Mr. Kim, and it is unclear how the relationship will factor into the speech.

Those teasers from the president, coupled with Mr. Trump’s propensity to change his mind, have made White House officials who have seen a draft of the speech cautious about saying definitively what will be in it in the end.

Mr. Trump’s prep work still pales in comparison to the effort some of his predecessors put into the State of the Union speech. For weeks leading up to the address, President Barack Obama would stay up late handwriting portions of his speech on yellow legal pads and bringing them to the Oval Office in the morning for his speechwriter to incorporate, according to former aides.

Mr. Trump does not write out his speech in longhand. But he is unusually involved in different drafts and updates, and he has a familiarity with the changing versions. In 2017, before his first address in front of a joint session of Congress, Mr. Trump grew frustrated when he realized he was reading off an old draft and that the latest revisions had not been incorporated into the text that he had been practicing.

“Why am I here?” he barked at his aides in frustration.

For a White House with a poorly organized policy process, the president’s interest in the State of the Union address has also become a helpful vehicle to try to set a legislative and foreign policy agenda. Last year, however, some of the promises that Mr. Trump made in his speech — uniting Republicans and Democrats behind a $1.5 trillion infrastructure plan, for instance — fell by the wayside as his interest in his own stated policies waned.

This year, there has also been concern among the president’s allies that Mr. Miller, who in previous years has bristled at losing control of the speech-writing process, has been trying to reassert himself as the final voice on a speech that will most likely lean heavily on immigration.