The District government’s budget cuts have hit home — or at least its alleys: The city has run out of garbage cans and recycling bins for its citizens.

On Dec. 6, Georgetown resident Ivy Pascal found her recycling bin missing from behind her Reservoir Road home. She called the city to order a new one and was told the bins were on back order. Every subsequent month, she called and got the same answer: No bins.

The situation is more dire than just back-ordered recycling bins. Nancee Lyons, a spokeswoman for the D.C. Department of Public Works, said last week that her agency has been out of recycling receptacles since the fall. The same goes for Supercans — the jumbo receptacles given to households that get once-weekly pickup — as well as the smaller, 32-gallon containers distributed in center-city neighborhoods that get twice-weekly trash collection.

The shortages are a consequence of a $3.9 million cut to the public works budget last fall, part of an effort by then-Mayor Adrian M. Fenty (D) and the D.C. Council to close a $188 million city budget gap for the fiscal year that started Oct. 1.

More containers are now on the way — 580 Supercans, 2,000 32-gallon recycling carts and 1,200 32-gallon trash cans — ­although there appears to have been some debate over whether that was going to happen. Lyons said last week that her agency was considering ending the practice of handing out free cans and bins. But that plan has been abandoned; it has registered among DPW management that eliminating trash cans wasn’t the place to slash $200,000.

“That wasn’t one of my best decisions,” said DPW’s director, William Howland, at a D.C. Council hearing earlier this month.

Linda Grant, another DPW spokeswoman, said Monday the agency recently ordered new trash and recycling containers. They are at least a month from delivery, however, and there is a significant backlog of can-seeking residents.

Since June, requests from more than 4,400 households pertaining to refuse bins have gone unfulfilled, according to city data. More than 1,200 desperate households have repeatedly asked for help. This month, city operators have fielded 571 requests, with 97 percent still waiting for satisfaction.

The city has provided residents with free garbage cans since 1980, when Mayor Marion Barry (D) introduced the Supercan as a money-saving means of converting twice-a-week trash routes to once-a-week service. Previously, residents kept their own trash cans — often of the stamped-metal variety famously favored by Oscar the Grouch of “Sesame Street.” It turned into an early triumph for Barry, and the 96-gallon plastic receptacles have become a beloved civic institution.

Under DPW’s currently posted policy, residents can pay $62.50 for replacement or additional Supercans — a price that’s held since at least 1995 — while recycling bins and 32-gallon cans are handed out for free.

But that only applies when there are cans to be handed out. So what is a binless resident to do? Pascal is using cardboard boxes salvaged from a nearby liquor store to hold her recyclables — which is a plan DPW endorses, said Lyons.

Pascal was less distressed about finding makeshift bins than about the advice she initially got from a city employee — which was to put her recyclables in with the rest of her landfill-bound trash. “I’m diligent about recycling everything,” she said. “I’m just sick that they’re announcing to everyone to throw everything away.”

It is, however, not city policy. “That doesn’t sound like anything our agency would tell a resident,” Lyons said.

Staff writer Luke Rosiak contributed to this report.