GOV. CHARLIE BAKER and the current and future mayors of Somerville took a joy ride on a portion of the new Green Line extension on Thursday — a preview of coming attractions as the $2.3 billion project nears completion.

The Union Square branch of the Green Line extension is scheduled to open in March and the branch into Medford is slated to start up in May. Both opening dates represent slight delays. But the big news is the Green Line extension, which early on had a price tag that soared to more than $3 billion, is now expected to come in under its $2.3 billion budget with enough money left over to reimburse Somerville and Cambridge for the $75 million they invested in the project and still have some cash in reserve.

Baker wouldn’t speculate on how much money will be left over, saying a lot of electrical work remains to be done, but he said credit goes to the way the T handled oversight of the complicated project.

Instead of giving responsibility to a small team at the T that also had other responsibilities to juggle, Baker said the decision was made to hire project manager John Dalton and a dedicated team of roughly 43 people who focused on the Green Line extension and nothing else.

“This is what they worked on. That’s all,” said Baker, who said the same approach is being used on construction of a commuter rail line from Boston to New Bedford and Fall River. Baker said the South Coast Rail project is also on schedule.

Somerville mayor-elect Katjana Ballantyne, who joined current Mayor Joseph Curtatone at the press availability at the new Lechmere stop in Cambridge, also provided a preview of what is likely to become a common refrain as the Green Line extension opens: How come it took so long?

Ballantyne took out a copy of the Somerville Journal from 2005. On the front page was a picture of her 7-year-old daughter, who spoke out in favor of the project at a meeting attended by former mayor Michael Capuano and then-MBTA General Manager Dan Grabauskas.

Ballantyne said her daughter came over to her after she spoke and asked: “Momma, when can I ride the train? I said maybe when you’re a senior in high school.”

Ballantyne added: “She’s 25 now.”