WASHINGTON — President Trump has invited representatives from cable and broadcast news channels to an off-the-record lunch at the White House ahead of his prime time speech Tuesday night, an address in which he is expected to frame his demand for border wall funding as a response to a national security and humanitarian crisis.

The White House has requested about eight minutes of broadcast time from the networks for Mr. Trump’s Oval Office remarks. The president appears to be preparing for the event as if he is delivering a miniature State of the Union message — typically, television anchors meet with the president over lunch ahead of his annual address to Congress.

As the partial government shutdown enters its third week, Mr. Trump’s aides have been making the case that there is a crisis at the border in briefings with staff members on the Hill and in meetings with journalists.

The White House has floated the idea of invoking emergency powers to build a wall along the country’s southwestern border without approval from Congress. But while Democrats have been bracing themselves for him to make that declaration on Tuesday night, administration officials who had seen a draft copy of his speech said the president was not preparing to do so.