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The executive branch and council members appear to agree that federal money is no longer a sure bet.

“Either we use local dollars to have these services provided, or we do not award those services at all,” Mr. Gandhi told members at Tuesday’s meeting.

Yet as host to the national government, the city’s financial potential is limited by unique planning rules and federal buildings it cannot tax - even if local crews are the first ones on the scene if one of them catches on fire.

Mr. Gandhi said the District is not subsidized by state appropriations, and its boost from the federal government does not always outpace its liabilities. He recalled the expansive view from his old office at Judiciary Square, where he could see federally controlled museums, galleries, monuments - “nothing we could tax.”

“That’s a major problem,” he said. “Not only that, but because of the height limitation, we cannot intensify or take advantage of the real estate we have. When I go to Wall Street, I come out of Penn Station and look at the high-rises there and say, ‘My God, the tax base!’ “

Rep. Darrell E. Issa, California Republican with oversight of D.C. affairs, has been speaking to Mr. Gray and Delegate Eleanor Holmes Norton, the city’s nonvoting member of Congress, about easing the height restrictions to increase living and working space - not to mention tax revenue - in the city as its population grows at a nation-leading pace, The Washington Post reported Thursday.

The money, Mr. Gandhi said, is needed to address the vast divide between the haves and haves-not in the city, where about a third of residents struggle with illiteracy, skyrocketing unemployment rates and lack of skills to seize on a number of jobs in the District.

“This is the nation’s capital - it’s a scandal,” Mr. Gandhi said. “We have to take care of this population ourselves with a constrained tax base, and that is the problem. What the city needs here is a recurring, regular, annual budget relief - and we don’t have that.”