The City of Boston’s House-approved bid to temporarily shift some of its property tax burden onto the business sector continues to stall in the Senate, where the top Democrat has raised questions about support for the bill and members gave a markedly muted response this week to an informal News Service poll asking for their thoughts on it.

Boston Mayor Michelle Wu has framed her plan, which has garnered extensive media coverage since she proposed it in April, as necessary to avoid a potential 33 percent hike in residential tax bills. But South Boston Sen. Nick Collins pointed Thursday to the city’s hulking rainy day funds as a way to smooth out the tax burden and said he has heard “so much opposition” to the mayor’s idea.

Given 48 hours to weigh in on the bill during the light-duty August recess, only nine of 40 senators or their staffs replied to the News Service’s inquiry, which asked whether lawmakers support allowing the City of Boston to temporarily shift its tax rates or whether they have concerns about the bill.

Of those nine, three said there were “concerns” around the home-rule petition, two indicated they were open to considering the proposal, and Senate President Karen Spilka’s office issued a new statement saying that she was “open to continuing conversations” with City Hall.

Three offices, those of Sens. John Cronin, Pavel Payano, and Michael Rodrigues, expressly declined to comment on the bill in response to the News Service’s question. Rodrigues chairs the Committee on Ways and Means which has held jurisdiction over the proposal since Aug. 5.

The lack of participation in the News Service’s poll, which provided two days for a response, could indicate that senators are undecided on the subject or that they do not wish to wade into a local matter that ballooned into a war of words between Wu and Spilka. Or, the silence of a majority of offices could also be a symptom of lawmakers’ traditional August vacation month.

Wu knocked the Senate on WGBH’s “Boston Public Radio” earlier this month, saying that if the bill is not enacted, “every single resident in the city of Boston will know that their taxes are going up because the Senate did not vote through that last step.”

A Spilka spokesperson shot back with a pointed critique of the bill: “Blaming the Senate may be politically convenient for the Mayor, but it does nothing to improve a policy proposal that has been widely questioned by fiscal watchdog agencies and could do serious damage to Boston’s economy.”

The president “has received no indication that there is sufficient support among Senators for this policy proposal to move forward,” the spokesperson said at the time.

In the post-July season of informal sessions, “sufficient” support can generally mean the ability to pass a measure without a single lawmaker objecting to its progress. Then again, few senators attend informal sessions, which typically unfold without a quorum present.

Collins, one of three to indicate reservations about the bill’s advancement, cited concerns about it from the business sector.

“We’re still hearing a lot of concerns that the legislation hasn’t changed, that has had so much opposition from the retail community, business community, and folks in general,” Collins said Thursday, “about taxes [going] up while the rainy day funds in Boston are double what they need to be, according to Moody’s.”

Sen. Michael Barrett of Lexington “has serious concerns about the bill,” his communications director, Ethan Raye, told the News Service.

And Senate Minority Leader Bruce Tarr of Gloucester “has concerns around this topic,” communications director Jessica Margiotta said.

Senate President Karen Spilka (Herald file)