The City of Boston’s attempt to temporarily shift some of its property tax burden to businesses, approved by the House of Representatives, continues to stall in the Senate. The top Democrat has expressed doubts about support for the bill, and lawmakers were decidedly cautious in their response to an informal News Service poll this week asking them what they thought about the bill.

Boston Mayor Michelle Wu has called her plan, which has received widespread media attention since it was unveiled in April, necessary to avoid a potential 33 percent increase in residential taxes. But South Boston Senator Nick Collins on Thursday pointed to the city’s ample reserves as a way to smooth the tax burden and said he had heard “a great deal of opposition” to the mayor’s idea.

Despite being given 48 hours to comment on the bill during the busy August recess, only nine of 40 senators or their staff responded to the News Service’s request for comment asking whether lawmakers support a temporary change in Boston’s tax rates or if they have concerns about the bill.

Three of those nine respondents said there were “concerns” about the home rule request, two indicated they were open to reviewing the proposal, and Senate President Karen Spilka’s office issued a new statement saying she was “open to further discussions” with City Hall.

Three offices, namely those of Senators John Cronin, Pavel Payano and Michael Rodrigues, declined to comment on the bill when asked by the News Service. Rodrigues is chairman of the Appropriations Committee, which has been responsible for the proposal since August 5.

The lack of response to the News Service poll, which allowed two days for responses, could indicate that senators are undecided on the issue or that they do not want to get involved in a local issue that has escalated into a war of words between Wu and Spilka. But the silence in most offices could also be a symptom of the traditional August vacation month for lawmakers.

Wu criticized the Senate earlier this month on WGBH’s Boston Public Radio, saying that if the bill does not pass, “every single resident of the city of Boston will know that their taxes are going up because the Senate did not pass this final step.”

A spokesman for Spilka countered with sharp criticism 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 financial regulators and could cause serious harm to Boston’s economy.”

The president had “received no indication that there was sufficient support among senators to advance this policy proposal,” the spokesman said at the time.

During the period of informal sessions after July, “sufficient” support can generally mean that a bill can pass without a single member objecting to its progress. On the other hand, few senators attend informal sessions, which usually take place without a quorum.

Collins, one of three who expressed reservations about moving forward with the bill, cited concerns from the business community.

“We’re still hearing a lot of concerns that the legislation hasn’t changed and that there’s so much resistance from the retail community, the business community and people in general,” Collins said Thursday. “According to Moody’s, taxes are being raised while Boston’s rainy day reserves are twice as high as they need to be.”

Senator 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 about this issue,” said communications director Jessica Margiotta.