“It’s almost as if I’m starting over again from a teenager,” said a woman who began delivering takeout dinners and groceries after being furloughed at the Department of Agriculture.

The shutdown is also hurting some of the most vulnerable, including the homeless and those who depend on federal rent subsidies.

Catch up: Over the weekend, President Trump proposed restoring temporary protections for the undocumented immigrants known as Dreamers in exchange for $5.7 billion for a border wall, an offer Speaker Nancy Pelosi immediately rejected. Senator Mitch McConnell, the majority leader, could propose legislation today that would wrap Mr. Trump’s proposal into a package to reopen the government.

News analysis: People who have done business with Mr. Trump say his current stance is consistent with negotiating tactics he used in the private sector: focusing foremost on claiming victory.