With debt payments, energy costs, federally mandated door-to-door service for the disabled, and employee health insurance driving MBTA costs up faster than its income, which comes chiefly from fares and a portion of the state sales tax, the T faced a deficit of $160 million for the coming year. The Patrick administration whittled that to about $60 million, partly through fare increases and service cuts that will take effect July 1, before asking legislators to make up the difference, mostly through a little-known surplus generated by statewide motor vehicle inspection fees.