Two members of the Massachusetts Department of Transportation Board of Directors on Monday said they are "reluctant" to put more money toward the Green Line extension project, and transportation officials unanimously supported a resolution that keeps project cancellation a major possibility.

This summer, transportation officials announced the estimated cost of the trolley extension through Somerville and into Medford had jumped from $2 billion to $3 billion and the MBTA estimated $742 million in "sunk costs" even if the state decides to cancel the project.

Members of the MBTA Fiscal and Management Control Board and the MassDOT Board indicated major reluctance toward chipping in more than the roughly $1 billion initially laid out, in addition to about $1 billion from the Federal Transit Administration.

"They're basically saying it's a good investment for the commonwealth at $1 billion, but it's not a good investment at more than that amount of commonwealth dollars," Transportation Secretary Stephanie Pollack summarized for reporters after members of both boards unanimously approved the resolution.

Asked what the chances are that the trolley extension would be built, Pollack said, "I don't want to predict."

Those holding the purse strings for the state said they would be reluctant to contribute additional Massachusetts taxpayer dollars for the increased project cost.

"I would be highly reluctant to invest any more money into this project," said Robert Moylan Jr., a member of the MassDOT board.

Betsy Taylor, another member of the board, said she is "reluctant to put additional money towards the Green Line extension."

Before discussing the resolution that would make the project contingent on funding from municipalities, developers and others, members of the MBTA's Fiscal and Management Control Board and the MassDOT board said they wanted local leaders to contribute.

"I keep hearing that you guys are going to put some skin in the game, and we're looking for that," said Russell Gittlen, a member of the MassDOT board, referring to leaders in Cambridge, Somerville and Medford.

Other means of achieving the project without an additional state expenditure would be through reducing the project's scope or finding more cost-efficient means of accomplishing the work.

In a Dec. 10 letter to Pollack, U.S. Rep. Michael Capuano of Somerville said he recognized that state officials faced difficult decisions, but urged that "any changes to the overall project should not prevent the delivery of long overdue, equitable transit options for residents living in the GLX area."

Capuano said he was proud of the role he played securing $1 billion in federal funds for the project. "I assume you will do everything humanly possible to ensure those hard-to-get Federal dollars are not 'left on the table,' " Capuano wrote.

Michael Norton contributed reporting.