The side of the trains say "T," but the people responsible for making them run - and run on time - work for Keolis Commuter Services, a subsidiary of the French national railroad, SNCF.

Inside Keolis's Boston office, you see the date "March 30" all over, including on stickers employees affix to their clothes declaring: "March 30 We can do this."

That's the deadline Keolis has set, and Gov. Charlie Baker's administration has accepted, for having 100 percent of service restored after a disastrous run of snowstorms and blizzards that forced hundreds of trains to be cancelled and left most others running late.

"Our goal is to have 100 percent full service by March 30, but I will say that we're assessing each and every day to see if we can make that a little bit sooner," Gerald Francis, Keolis' general manager in Boston, said in an interview Thursday. "We're working diligently to make that happen."

One of the biggest challenges, Francis said, is that as many as 15 locomotives had traction motors ruined by choking snow. The service needs 63 operable diesel-electric locomotives to guarantee 100 percent of service can be operated, but as of midday Thursday, only 46 were in service. Locomotives may need as many as four traction motors replaced, and each repair session can take two or three days, plus testing afterwards.

The warning it could take a whole month to get the system from 80 percent to 100 percent service has not set well with riders.

"That's a little disappointing, especially for a lot of commuters around here," said Casey Franklin of Canton.

Melanie Hedlund of Lexington, who takes the train from Belmont to North Station every workday, said she was annoyed by the warning it would take a solid month to restore full service.

"That's why I didn't buy a March pass," Hedlund said. "My commute is 45 minutes longer each way. I'm adding an hour and a half commute without getting paid for it. I'm not so happy about that."

Francis said he's talked to many T riders and understands why they are so frustrated and disappointed.

"The mechanical guys are doing their darnedest, and I can tell you, all the employees here want to make sure we have full service by March 30," Francis said. "We're assessing each and every day the possibility that, if we can bring service sooner, that's what we're going to do."

With videographer Brian Butler