A sign hangs on the door of the Smithsonian National Museum of American History stating that the museum is closed because of a partial government shutdown in Washington on Jan. 2. (Saul Loeb/AFP/Getty Images)

NEW YEAR’S DAY has come and gone, with agencies encompassing 25 percent of the federal government — from the National Park Service to the Justice Department — still shut down because of a budget impasse soon to enter its 13th day. This is an inconvenience for tourists and a headache for federal workers, hundreds of thousands of whom must either work without pay or go on furlough. For the most vulnerable members of the federal workforce, however, the shutdown represents outright hardship.

We refer to the maintenance, security and food­service personnel who staff the entrances and cafeterias of federal buildings. You don’t necessarily notice what they do, because much of their work takes place after hours, when civil servants have gone home and their trash cans need emptying and floors need polishing. It’s important work nevertheless, albeit often paid at or around minimum wage by the companies that contract with the government to provide these services. Like civil servants, hourly workers for government contractors do not collect their pay during shutdowns; unlike civil servants, however, they do not get back pay when the shutdown ends.

How many low-wage workers face this predicament is difficult to ascertain, though perhaps fewer than in some past shutdowns, which affected more agencies. Still, The Post reports that the number could be approximately 2,000, based on estimates from the union that represents many such employees. Past efforts to legislate earnings protections for these humblest of federal workers have come to nothing, and it’s a difficult problem because any solution that makes workers whole would inevitably require the government to pay for services it did not receive. On the other hand, perhaps the prospect of having to do just that might help deter future shutdowns, if only a little.

Certainly we could all use a bit more urgency about getting out of this one. President Trump made it clear Wednesday there will be no settlement until he gets his way on funding for a border wall, and Democrats seem determined not to cut a deal with him until the House, which they won in November, has an opportunity to vote for the Democrats’ preferred solution. This would consist of two measures: one to fund departments such as Agriculture and Interior through Sept. 30, at levels already accepted on a bipartisan basis by the Senate; and another to fund the Department of Homeland Security, at current levels, including $1.3 billion for border security, through Feb. 8 while the parties continue to haggle.

Though a reasonable proposal on its face, the Democrats’ idea has no chance of even being considered by the Senate, because Mr. Trump has said he won’t settle for less than $5.6 billion in new wall funding — and Majority Leader Mitch McConnell (R-Ky.) has said he won’t bring any bill to the floor unless the president supports it. As we have said before, the likeliest face-saving compromise would be one that gives Mr. Trump more wall funding in return for a permanent solution to the plight of a vulnerable population: the undocumented-but-American “dreamers.” Meanwhile, the standoff continues, and yet another vulnerable population pays the price.