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Mr. Mendelson went out of his way Tuesday to stress that the city is employing a “two-track strategy” to support friendly members of Congress in their legislative efforts. He also said the council’s move appears to be legally sound, even if some officials are skeptical about their ability to intrude on congressional powers.

“We don’t cut them out of the [D.C. budget] process,” Mr. Mendelson said. “We would approve the budget like any other act — which goes to the Hill — and Congress has plenary authority over the District. They could pass a bill tomorrow that changes anything we do.”

The Home Rule Act lists a number of subjects the city’s lawmakers may not touch, but “the budget process is not one of them,” he said from the council dais.

He said the District used the same mechanism to make the D.C. attorney general an elected office, beginning in 2014. The referendum went before Congress, but no one on Capitol Hill objected during the 35-day review period.

Mr. Zherka said the council’s latest effort is about overcoming hurdles from a minority of federal lawmakers who have put up roadblocks to D.C. budget autonomy.

“I don’t think we’re going to win by waiting for something to happen,” Mr. Zherka said. “I think the District understands that it has to start doing some things on its own.”