But at a time when a president is typically finishing a collection of policies in connection with the State of the Union and previewing them to build public support, some of Mr. Trump’s aides acknowledge that the president and his senior team have been almost entirely focused on the border dispute.

Indeed, administration officials said the situation had the unintended benefit of making it easier for Mick Mulvaney, the newly installed acting White House chief of staff, to settle into his job because he did not have as many issues to juggle.

The president, who made no public appearances on Tuesday, has kept his primary attention on the fight for the border wall for weeks, making only two unrelated out-of-town trips since the shutdown began, an unannounced stop in Iraq to visit troops at Christmas time and a quick flight to Dover Air Force Base in Delaware last weekend to pay respects to the returning remains of four Americans killed in Syria. Even a day trip to New Orleans to address farmers turned into another public pitch for the wall.

Still in his inbox are a slew of important vacancies to fill, including defense secretary, interior secretary and chief of staff. His attorney general, United Nations ambassador and Environmental Protection Agency chief are all serving in an acting capacity while waiting for Senate confirmation votes of his nominees. The White House on Tuesday sent 51 judicial nominations to the Senate, returning names that had gone unacted on last year.

Mr. Trump expressed no urgency when asked by reporters recently about all the acting officials in the upper echelon of his administration. “I like acting,” he said. “It gives me more flexibility.”

Left uncertain is how Mr. Trump may pursue other goals. He vowed before the midterm election to pass a middle-class tax cut in the new Congress but has said little about it since then. He also vowed to pull out of the North American Free Trade Agreement to pressure Congress to pass his newly negotiated replacement but has yet to do so.

He has similarly talked about collaborating with Ms. Pelosi’s Democrats, who just took over the House, on possible bipartisan initiatives like rebuilding the nation’s roads, bridges and other infrastructure or bringing down the cost of pharmaceutical drugs. Neither of those ideas has come up lately and it is hard to see the current impasse establishing the sort of trust that might lead to across-the-aisle cooperation.