(Image Credit: @Liz_Cheney/Twitter)

Former Vice President Dick Cheney expressed his gratitude today to the family that donated the organ he received during a heart transplant at the end of March.

"It's the kind of gift that's unbelievable," Cheney said, speaking at length to student interns at the Washington Center and broadcast on CSPAN. Despite the recent surgery, Cheney was alert and engaged, though his voice was seemed a bit huskier than usual.

Cheney was released from Fairfax Hospital in Virginia April 3. He said following the surgery his health is the best it has been in a long time. Procedures leading up to the transplant began back in July 2010, Cheney said, when his heart was still pumping but could not provide enough blood to vital organs like his kidneys. At that time, Cheney underwent surgery to implant an LVAD ,  or a Left Ventricular Assist Device, which he said revitalized his organs enough to withstand the trauma of a transplant while also delaying the need for one.

Cheney described having to wait on call for an organ to be ready, saying there are "not enough organs" to fit the need in the United States. He also indicated that the heart must have the correct blood type and a size that was appropriate for the recipient's body. At midnight on the night before the surgery, Cheney said he and his wife received a phone call, telling them to come to hospital for the procedure, which began at 7 a.m. that morning. He said it lasted five to six hours and ultimately left him feeling much better.

Read more about that surgery from ABC News' Jonathan Karl HERE .

Cheney said he was "very, very fortunate to receive" the heart. He emphasized that when one person becomes a donor, the recovered organs can help several people, not just one. "It might be eight or 10 people who benefit," Cheney said.

The New York Organ Donor Network says one organ donor can "save up to eight lives" and donating tissues and corneas can help "up to 50 people."

Cheney said he would "encourage people to participate" in the organ donor program, but he said, "that's a personal decision, of course."

Cheney himself is an organ donor, saying his license has a red heart to indicate that.

Cheney also spoke about habits he had while working in government that contributed to his bad health.

He said he smoked two to three packs of cigarettes per day up until he suffered from his first heart attack in 1978.

"Drinking a lot of black coffee, smoking cigarettes, not getting enough sleep or exercise" and spending long hours at the office all had a part in harming his health.

"What I didn't understand until later was that there was such a thing as quality and that it was important not just to be at your desk, sending memos out and responding to memos," Cheney said. Taking time off with family and delegating tasks to good staff are also pivotal to success, the former vice president indicated.

Asked by a member of the audience how young people should deal with disagreements they might have with bosses, Cheney talked about same-sex marriage.  His daughter Mary is gay and outspoken in backing same-sex marriage, but Cheney said he was not about to challenge then President Bush's stance on the issue.

"He's the boss. He got elected. You didn't," Cheney said.

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