BOSTON – Advocates pushing for an underground rail connection between Boston’s North Station and South Station met at the Statehouse on Monday to help organize public support for the proposal.

The group is hoping to persuade Republican Gov. Charlie Baker to consider the rail link, which they say would provide for the possibility of uninterrupted Amtrak passenger service between Washington, D.C., and Maine.

Former Govs. Michael Dukakis, a Democrat, and William Weld, a Republican, have endorsed the plan.

Dukakis, speaking with reporters after a meeting of the North South Rail Link working group, said the next step is “lots of advocacy, lots of debate, lots of discussion.”

Baker – who met privately with Dukakis and Weld earlier this month about the proposal – has expressed skepticism, saying after that meeting that he needs more time to study the idea, adding that “the devil is very much in the details.”

Baker has expressed interest in a plan to expand South Station, which he said has other benefits, like opening up Dorchester Avenue and developing an area along the Fort Port Channel near downtown Boston.

Dukakis said the money spent on that project would be better spent on the rail link, which supporters say will also unite the north, south and western branches of the state’s commuter rail system.

Baker has said he doesn’t see expanding South Station as an alternative to the rail link, adding that the South Station project “is something we will and absolutely should consider.”

Key to gaining traction for the North-South rail link is to build support among members of the public still leery of big transportation projects in the wake of the massive Big Dig highway project through downtown Boston.

Dukakis said that the rail link proposal is nothing like the Big Dig.

Among those on the rail link’s working group are several mayors, including Somerville Mayor Joseph Curtatone, Salem Mayor Kim Driscoll, Quincy Mayor Tom Koch, Fitchburg Mayor Lisa Wong and Newton Mayor Setti Warren. There are also a handful of state lawmakers and Massachusetts AFL-CIO President Steven Tolman.

Dukakis said the project has the backing of two-thirds of state lawmakers. He said the group plans to meet monthly.

The rail-link idea is nothing new. The concept that has been discussed off-and-on for decades.

The proposal has resurfaced as the state continues to grapple with the failure of the public transit systems during last year’s historic snowfalls and a report that another major project – the expansion of the Massachusetts Bay Transportation Authority’s Green Line to Somerville and Medford – could cost up to $1 billion more than planned.

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