The stimulus windfall soon to land in D.C.’s lap will not be enough to solve the city’s formidable financial challenges, but District leaders said Wednesday that the final version will likely include hundreds of millions that could help balance the budget.

The House and Senate have passed competing versions of the American Recovery and Reinvestment Act — the Senate designated roughly $922 million for D.C. and the House nearly $1.1 billion. Chief Financial Officer Natwar Gandhi told the D.C. Council on Wednesday that roughly a third of the final figure may be available for general fund needs, like closing the estimated $455 million gap in the upcoming budget.