(Sarah L. Voisin/The Washington Post via Getty Images)

If the federal government shuts down next week, the nation's capital may have a trash problem on its hands.

Washington, D.C., is in the unenviable position of being treated like just another federal agency in the event of a government shutdown. Only "essential" employees are allowed to keep working, and that means some of the finer things in life won't continue for residents of the city.

It's very likely that trash collection will stop for one week, street cleaning will be on hold indefinitely, public libraries and the Department of Motor Vehicles will all close on Oct. 1 until Congress fixes its budget problems.

That prospect has D.C. city officials, who for years have been peeved that Congress controls the city's purse strings, pretty upset.

At a breakfast meeting with D.C. Mayor Vincent Gray this morning, they openly discussed the prospect of defying the federal government by continuing to operate even if the government does shut down.

And the City Council Chairman told ABC News that the council would meet next week to pass a resolution that keeps the government open - an act of "civil disobedience" - as Gray termed it in this morning's meeting, reported the Washington Post.

"The sentiment was pretty clear that we want to do everything we can to keep the government open," D.C. City Council Chairman Phil Mendelson told ABC News in an interview. "And make it clear to Congress that the nation's capital cannot function with the current financial relationship that requires that Congress, which really could not care less about the District's budget, to have to approve the budget before we can spend it."

If Congress fails to act, the government will run out of money at midnight on Sept. 30. The next day, the council plans to pass a resolution that would essentially make all city government employees "essential" employees, so that they'd be eligible to work though a shutdown.

The problem for city law makers is that defying Congress carries stiff penalties under federal law, including a fine of up to $5,000 or up to two years in jail, or both.

Despite that, Mendelson said he doubts council members will be arrested for violating that law.

"Is the mayor going to be put in jail because he came to work? No," Mendelson said. "I just don't think that's what's really going to happen here."

Gray, however, has been arrested in the past. In 2011, he, along with other protesters, were arrested in front of the Capitol for protesting additions to a budget deal that restricted the city from spending money to pay for abortions for low-income women, and to fund a needle exchange program used to combat the spread of HIV.

According to the contingency plan for a government shutdown that Gray's office released the last time the city was threatened with a shutdown in 2011, police officers, emergency personnel, schools and some health and human services functions will continue to operate in the event of a shutdown.

Last week, D.C.'s delegate to Congress Eleanor Holmes Norton asked House Speaker John Boehner, R-Ohio, and Senate Majority Leader Harry Reid, D-Nev., to leave D.C. out of the budget fight being waged in Congress.

The proposal would mirror one that she helped pass in the winter - the 1995 government shutdown that allowed the D.C. government to stay open.

"The city is an innocent bystander in this federal fight, but a local D.C. shutdown will amount to a great deal more than collateral damage," Norton said in a statement.

So far, those requests have not been granted.