Councilmember Helena Brown, who represents District A, issued a statement saying the city is faced with a dire financial situation and could find itself bankrupt by July of next year.
Brown is known for being a dissenting voice at city hall and for frequently voting against expenditures in the city.
"The facts are that the city is running a $2.4 billion deficit, of which over $271 million was added in 2011 alone."
Brown says the mayor's proposed budget isn't flat and the city is spending beyond its means.
In response to questions from reporters, Mayor Annise Parker says the city is well-run, gets excellent financial ratings and she doesn't know what Brown is talking about.
"I don't see it. I don't know of a credible professional that sees anything wrong with the City of Houston's finances. We have an annual audit done each year, anybody can go and look at the audit."
Parker acknowledges the city has mounting pension fund obligations that it must work out with the city's unions. But she says that has nothing to do with the city's general fund budget and says the city is in no danger of bankruptcy.
City council will be briefed on the budget in the coming weeks and then will offer their amendments before a vote on a final version in June.