In addition to funding government operations through Feb. 16, the House-passed bill would extend funding by six years for the popular Children’s Health Insurance Program, a provision intended to secure Democratic votes.

But Democrats were seeking concessions on other priorities, such as protecting young undocumented immigrants from deportation, increasing domestic spending, securing disaster aid for Puerto Rico and bolstering the government’s response to the opioid epidemic.

Federal agencies had prepared for the shutdown; on Thursday night, officials at the White House Office of Management and Budget instructed federal agency leaders to give their employees informal notice of who would be furloughed and who would not if funding lapsed.

Formal notifications are to be given as early as Saturday morning, budget office officials said, insisting on anonymity to brief reporters about the details of what the White House called “lapse planning and shutdown operations.”

More than one million active-duty military personnel will serve with no lapse, they said, but could not be paid until the shutdown ends. Agencies like the Energy Department that have funding that is not subject to annual appropriations can use that money to stay open, the officials said, and the administration is encouraging them to do so. Most mandatory programs — entitlements such as Social Security that are automatically funded rather than subject to congressional appropriations — can continue without disruption.

Officials said Mr. Trump may travel on Air Force One to carry out his constitutional responsibilities, including a planned trip next week to Davos, Switzerland. But it was unclear whether trips to Mar-a-Lago — his exclusive club in Palm Beach, Fla. — such as the one he had planned for this weekend, would fall into that category.