WASHINGTON — Less than two weeks before much of the government runs out of money, President Trump on Tuesday escalated the threat of a shutdown, accusing Democratic congressional leaders of plotting to use their leverage to raise taxes and flood the country with undocumented immigrants.

The Democratic leaders, Senator Chuck Schumer of New York and Representative Nancy Pelosi of California, responded to the president’s provocations by pulling out of a scheduled White House meeting meant to address the thorny issues that lawmakers are facing as the end of the year approaches.

Mr. Trump then doubled down, posing for television cameras at the White House next to empty chairs and calling his would-be negotiating partners weak on crime, weak on immigration and weak on the military.

“They’ve been all talk, and they’ve been no action, and now it’s even worse,” Mr. Trump said. “Now it’s not even talk.”