But the bill’s $38 million price-tag drew scrutiny.

Critics said the money would be better spent on targeted tax relief for the poor and middle class or on programs addressing homelessness or economic inequality.

And there’s not much money to go around. A report released last week showed that the District will see almost no revenue growth this year because of a slowing economy and fallout from the federal government shutdown, leaving lawmakers bracing for a tough budget cycle.

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The council unanimously voted Tuesday to send the legislation back to the Finance and Revenue Committee. The action came after a breakfast meeting of the council, where seven of 13 members spoke against the bill.

Some questioned whether homeowners in the wealthiest parts of the city need an extra $400 a year.

“Frankly, it’s a dinner or two at Le Diplomate for them, but it adds up to a lot of money for us in terms of costs,” said council member Elissa Silverman (I-At Large), referring to a popular French restaurant on 14th Street NW in Logan Circle.

The homestead tax deduction allows homeowners to avoid paying residential real estate taxes on the first $74,850 in assessed value for their primary residence. The bill would raise that threshold to $125,000, which translates to a flat savings of about $400 regardless of the home value.

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Council member Robert C. White Jr. (D-At Large) proposed an alternative version of the bill that would expand a separate Schedule H tax credit for low-income renters and owners.

But Todd, who said many constituents in his Northwest Washington ward have been priced out of their homes, defended the idea of a broad-based tax cut.

“When we created homestead in 1978, we created it for every person . . . not just certain people,” Todd said. “This notion that I’ve been hearing over the last couple of weeks that we can’t help every single taxpayer, it really isn’t fair. It’s not being inclusive.”

A group of activists led by the left-leaning D.C. Fiscal Policy Institute organized at city hall to lobby lawmakers against the bill.

“D.C. already has the lowest residential property taxes in the region, and the District’s property tax includes many mechanisms to protect low-income homeowners and older residents from burdensome property taxes,” said Ed Lazere, the executive director of the institute.

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Some, including Chairman Phil Mendelson (D), floated the idea of passing the bill and budgeting for it in a future year. But others lawmakers feared the mixed messaging of passing a tax cut without actually cutting taxes.

“It’s going to be very confusing,” said council member Charles Allen (D-Ward 6).

Council member Jack Evans (D-Ward 2) suggested money lost through the tax cut could be recovered because the city was expecting higher property tax revenue as housing values rise.