The D.C. Council, seen here in May debating the mayor’s homeless shelter plan, approved closing D.C. General on Tuesday and put the city on a collision course with Congress over city spending. (Ricky Carioti/The Washington Post)

The D.C. Council pressed forward Tuesday to declare fiscal independence from Congress, approving a $13.4 billion spending plan despite a vote by House Republicans last week warning District leaders against the action.

With the unanimous vote, the District is poised to implement a 2013 ballot measure approved by voters that empowers city leaders to spend local tax dollars without explicit congressional approval — acting more like an independent state than a federal territory controlled by Congress.

House Republicans last week passed a measure calling the move a violation of the Constitution and the authority it gives Congress to oversee the District. On the day of the vote, House Speaker Paul D. Ryan (R-Wis.) said the “current D.C. government needs to be reined in.”

The council also approved a plan to close the city’s dilapidated family homeless shelter at D.C. General Hospital and replace it with a network of seven smaller shelters to be constructed in neighborhoods across the city.

Despite months of heated arguments between the mayor and the council over details and continued criticism from residents, D.C. officials are moving ahead with the project, which is slated to cost almost a half-billion dollars over 25 years. It is the city’s biggest effort yet to address a growing crisis of homeless families.

Speaking after the votes, D.C. Council Chairman Phil Mendelson pursed his lips when asked about the escalating conflict with Congress. He said he thought the city would prevail in its fight with House Republicans, either because the Senate will decline to take up the House bill or because any potential legal challenge by House members would fail.

“I’m hopeful that the members of Congress will realize that they are actually hurting us, financially,” said Mendelson (D), referring to the higher borrowing costs the District faces when it has to wait for Congress to approve its spending. Congress has tied up the District’s spending for 20 consecutive years by failing to pass a federal budget on time, he said.

“We can do this ourselves, and we can do it better than them,” Mendelson said.

It will mark the first time the city has opted against submitting its budget to the president for inclusion in the federal budget, like that of an executive branch agency. In the past, Congress has used the federal budget process to attach riders to the District’s spending plan that affect local laws. Among other changes, Congress has prevented the city from fully legalizing marijuana and from subsidizing abortions for low-income residents.

Instead, the city will send its budget directly to Congress. Unless both houses and the president object within 30 legislative days, the budget will be considered approved and will take effect in October.

But the dispute with Congress is far from over. Last week, a House subcommittee attached a rider to a federal budget bill that would repeal the city’s 2013 referendum on budget autonomy. Congress must pass a spending bill to keep the federal government running past Sept. 30.

The D.C. budget approved Tuesday continues the city’s record spending on education and social services of the past five years and also directs a share of growing revenue back to taxpayers under a schedule of tax cuts approved two years ago.

New items in the District budget include a $1 million pilot program to give families at risk of falling into homelessness debit cards loaded with city funds to help them try to stay out of shelters.

The budget also includes a provision adopted by 42 states that says if city firefighters were healthy nonsmokers when they were hired and they later develop cancer, it can be categorized as job-related. The bill was passed five years ago, but then-Mayor Vincent C. Gray did not implement it, saying it would be too costly. Mendelson used data from other states to convince city financial officers that the cost would probably be lower than originally forecast.

In a letter about the budget to council members, Mayor Muriel E. Bowser (D) did not object to the provision for firefighters but said the overall spending plan “goes too far” in cutting her proposals for public safety, sidewalk and alleyway improvements, and other projects, including cafeteria renovations at Shepherd Elementary School in her home ward.

The council approved a proposal Tuesday by her successor, council member Brandon T. Todd, to shift money from elsewhere, including $1 million for snow and trash trucks, to keep the project on track. The change came despite Bowser’s warning in her letter that “broken and substandard equipment” could mean slow snow removal next year or even trash collections “missed entirely.”

The budget also fully funds the new shelter system, including an estimated $105 million in construction and land purchases in the coming year.

At Bowser’s request, the council moved its planned Ward 6 shelter to 850 Delaware Ave. SW, a city building now used as a community health clinic but that is in need of major repairs. A council plan to build on a parking lot over Interstate 395 would have taken too long to open the shelter in an expedited manner, Bowser said in another letter to the council last week.

The council also settled on situating a homeless shelter at 1700 Rhode Island Ave. NE, replacing Bowser’s plan for one in a Ward 5 industrial area heavily criticized by homeless advocates.

The council also voted Tuesday to increase the size of another shelter on Idaho Avenue in upper Northwest.

Bowser, who hurled an expletive at Mendelson over changes to the plan two weeks ago, thanked him in a statement, saying that the debate is “now behind us” and the task is building shelters “that we can all be proud of, and that reflect the best of who we are as a society.”