The Democratic-controlled Massachusetts House has voted to back a plan by Republican Gov. Charlie Baker to close a projected $768 million state budget shortfall.

The deficit-reduction plan was approved on Wednesday by a near-unanimous vote and sent to the state Senate.

The plan includes a $40 million cut in state transportation funds, coming at a time when a series of recent winter storms has snarled traffic and caused major disruptions on the MBTA.

House Ways and Means Committee chairman Brian Dempsey offered assurances that the budget reduction would be to administrative overhead and not further impact service on the T.

Baker's proposal would also create a tax amnesty program for corporations and use $131 million in capital gains tax revenue that would have otherwise been deposited into the state's rainy day fund.