While other state legislators were listening to new Gov. Dannel P. Malloy talk about the state’s financial challenges, Norwich state Rep. Christopher Coutu was listening to the beeps and screams of medical monitors attached to his newborn baby at Boston Children’s Hospital Cardiac Intensive Care Unit.

Alexandria Grace Coutu was born to Chris and Neringa Coutu on Dec. 28 at Bringham & Women’s Hospital in Boston on Dec. 28. Her parents have known for months that Alexandria suffered from a ventricular septic defect and transposition of the great arteries.

As Chris Coutu described it, “the main arteries are backwards, so oxygenated blood circulates to and from the lungs, but not to the rest of the body.”

The Coutus kept quiet about the birth of “our little angel," their first child, for a few days until she underwent six hours of surgery on New Year’s Eve. A relieved and exhausted dad said the surgery went extremely well, as successful as anyone involved could imagine.

Within days, all the tubes and intravenous lines were removed from her tiny 7-pound frame and amazingly, all three expect to come home soon.

“She’ll have a cardiologist for the rest of her life, but we couldn’t hope for a better outcome,” Chris Coutu said.

Just as impressive is the gift Alexandria’s dad presented to his newborn daughter and to the family’s hundreds of supporters and well wishers.

“My First Week of Life, A Gift from Dad” is a four-minute video and slide show Coutu placed on his Facebook page that chronicled Neringa’s pregnancy, the frightening diagnosis highlighted on an early ultrasound, her birth, emergency surgery, and the face of a happy newborn baby girl dwarfed by a city of high-tech machines, monitors, tubes and electronic equipment.

The video ends with a message from Alexandria, thanking all her doctors, nurses and the two hospitals “for a second week of life.”

“I didn’t’ know what the outcome would be,” Coutu said of his decision to film these critical events, not knowing whether little Alexandria Grace would survive. “I just made a decision early on that I would take some pictures and videos so she could see it. It really ended up being such a special gift to her. It’s a cool video.”

That it is.