BOSTON — Now comes the hard part for the new board overseeing the T.

The MBTA Fiscal Management and Control Board, created in the state budget signed into law by Republican Gov. Charlie Baker last month, is quickly confronting difficult operational and political choices it may be forced to make while grappling with its mission of stabilizing the antiquated, debt-ridden transit system so badly exposed during last winter’s record snows.

Case in point is the long-delayed extension of the Green Line to Somerville and Medford, which threatened to again go off the rails with recent word from the Massachusetts Bay Transportation Authority that the state’s share of the cost could jump as much as $1 billion.

Baker has warned the project cannot be pursued at any cost or at the expense of transportation infrastructure needs statewide. The governor’s transportation secretary, Stephanie Pollack, said all possibilities would be weighed including cancellation of the project, though she stressed that was not the desired option.

Any move to scrap or significantly scale back the 4.7-mile Green Line extension could be fraught with political and even legal consequences. Supporters have long touted the project as a key economic boost for a region popular with young professionals and students but historically lacking in mass transit.

The project has been on the drawing board for more than two decades since the Conservation Law Foundation, as part of an air pollution mitigation agreement that allowed the state to move forward with the massive Big Dig highway project, won a commitment for an array of public transportation improvements. Abandoning the extension could invite a legal challenge from the organization.

What’s more, the Federal Transit Administration last year committed nearly $1 billion to help fund the project, money likely forfeited if the state doesn’t move forward.

It’s but one dilemma facing the five-member control board, which is scheduled to hold its next meeting on Monday.

Creation of the board, which will oversee the MBTA for at least three years, was recommended in April by a Baker-appointed task force that found the transit system to be in “severe financial distress,” with ineffective management and no viable maintenance and repair plan for equipment.

The Legislature agreed to establish the board despite reservations from some top Democrats who felt Baker already had the tools at his disposal to fix the T. Lawmakers also granted Baker’s wish that the agency be given more flexibility to outsource some functions to private vendors, but stopped short of giving the board greater power over collective bargaining agreements or the ability to raise passenger fares beyond current state-imposed caps.

Ultimately the control board may have to balance visions of future service enhancements with funding constraints and the need to bring current assets up to par – especially with another winter fast approaching. Hanging in the balance would be not only the Green Line expansion project but others proposals such as SouthCoast commuter rail that have lingered in the pipeline for years.

A traffic study released this week by the Texas A&M Transportation Institute and INRIX Inc., placed Boston among the nation’s top ten most congested commuting cities. Transit advocates see new rail options as alternatives to ever-growing gridlock, but the governor’s review panel criticized the MBTA’s past expansion strategy as “shortsighted,” saying the state has spent billions on new projects while the system’s overall “state of good repair” backlog – most recently estimated at $6.7 billion – continues to grow.