Beacon Hill's past and present met at the State House Wednesday to discuss something that could dramatically change Boston's future: a proposed tunnel under downtown that would connect North and South Stations and allow train travel through the city.

Former governors Michael Dukakis and William Weld pitched the idea of a North-South Rail Link to current Gov. Charlie Baker at an afternoon meeting. The bipartisan duo says building the tunnel would decrease congestion and greatly improve rail transit in Massachusetts as well as up and down the East Coast.

"You're facing a severe congestion problem at not one, but two train stations," Dukakis told reporters outside his old office after the meeting. "You can't postpone it. You can't shove it under the rug here."

Because the two stations are not connected, Amtrak passengers need to get across town from one station to the other if they want to travel through Boston. The project would use modern tunneling technology to dig under the city from around Widett Circle (Widett lives!) to the other side of the Mystic River, according to Baker.

Before you get too excited and/or furious, let The Duke assure you, it's not like a certain highway project begun under his administration.

"This is not the Big Dig, folks," Dukakis said, assuring the press, as he had assured Baker, that the project is feasible and would cause little disruption. "This is very different,"

The ex-governors sit down with Baker comes after the MBTA's disastrous winter and news that the under-construction Green Line Extension to Medford could be $1 billion over budget.

But with a cash-strapped MBTA, Baker unconvinced about a projected $2 billion to $4 billion dollar price tag and voters weary of increased taxes, the project remains on the drawing board for now. Dukakis and Weld will launch a planning group to further study the proposal on September 21.

For his part, Baker heard Weld and Dukakis out, but said he would be cautious with the state's money.

"My view on this, and said this to both governors, is that when it comes to projects like this, the devil is very much in the details," Baker said. "And while it's not possible, necessarily, to get every answer to every question, because in many cases they're not all answerable all at once, these are projects that should be treated with a high degree of respect and we plan to treat it that way."

The idea for a North-South Rail Link has been kicking around for over a century. The goal is to connect Boston's North Station to South Station, uniting the city's two major rail hubs and linking train service from points south of Boston all the way north into Maine. To travel north of Boston via rail from points south today, passengers must travel from South Station to North Station and vice versa by either the MBTA (via a subway line change at either Downtown Crossing or Park Street) or automobile.

Proposals on how to get from one station to the other have differed over the years, but one current proposal would call for a tunnel to be built under downtown Boston wide enough for at least two train tracks between the stations.

Dukakis, the Commonwealth's longest serving governor and Democrats' presidential nominee in 1988, has been an advocate for the rail link since his days in office. Weld is a more recent convert, at least in publicly backing the project, but has backed the idea for some time.

In a recent Boston Globe op-ed, the two former governors argue the MBTA's recent winter failures should not slow the state from expanding rail development.

"If the Massachusetts economy is going to continue to grow and create good jobs for our people, making that system better must be our top priority," Dukakis and Weld wrote.

The bipartisan duo also claim the tunnel would pay for itself in new passenger revenue, maintenance savings and by eliminating the need to expand South Station.

The Governor Michael S. Dukakis Transportation Center at South Station, named after the Duke just last year, is the subject of a massive proposal to expand onto land currently under the control of the U.S. Post Office in order to build new tracks, alleviate congestion and expand service.

Dukakis thinks expanding the Dukakis Center is a bad idea.

Both former governors arrived well ahead of time for the scheduled 2:30 p.m. meeting in their old office, now Baker's. Dukakis, 81, arrived first and Weld, 70, climbed Beacon Hill by himself in the 93 degree heat and declined to comment to a reporter on Park Street and to press arranged outside the governor's office.

The state Legislature last year authorized the governor to spend up to $2 million in bond funds to update dusted-over environmental reports for the rail link's right-of-way.

Baker hasn't touched that money or pursued the updates, the State House News Service recently reported. According to SHNS, Massachusetts Department of Transportation spokesman Michael Verseckes admitted in an email that "… MassDOT has not spent money to update or advance this study referenced in the bond bill."

Even Amtrak is short on ideas of how to get its passengers between the stations. On the rail service's website, Amtrak informs riders that passengers "transferring between the Downeaster and other Amtrak services must make their own arrangements for the transfer between stations in Boston." And Amtrak's suggested mode of transportation between the stations? Boston's famous taxi fleet, of course. That's right: Get off the train, hail a cab, then get on the other train across town.

"When transferring by taxi it is suggested that passengers connect to their continuing Amtrak train at South Station," the website says. "Transfer by taxi is recommended for passengers traveling with significant amounts of luggage or young children."