"She couldn't quite hold it, but it was there," Woods said at a press conference on Tuesday to kick off the AT&T National Golf Tournament in Bethesda, Md., which he's hosting this week.
The golf champ, 31, talked about how his life has changed since he and wife Elin Nordegren welcomed Sam on June 18th.
"It's been fantastic these last couple weeks to have Sam Alexis as part of our life," he said. "It was a dream come true for both Elin and myself. I've been changing diapers and doing feedings. I definitely don't sleep now."
His late father, Earl Woods, used to call him Sam, he said, which is why they chose the name. "We wanted to have a name that would be meaningful. My father had always called me Sam since the day I was born. He rarely ever called me Tiger."
Nordegren, 27, was in a Florida hospital for several days due to complications before she gave birth while Woods competed in the U.S. Open in Oakmont, Pa., he revealed. "We talked all the time. Everything was alright. It wasn't life threatening or anything. She just had a few problems and had to be admitted.
"It wasn't easy. It was not easy because I wanted to be there. And the doctor and Elin said, 'There's nothing you can do. So go out there and just get a W [a win].' Well, I came close," said Woods, who finished second in the tournament. "But that night was infinitely more rewarding than any W ever could have been."
Asked how he was able to focus on his game under the circumstances, Woods said, "You just do. You just do."
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When one reporter asked whether the fact that Woods is an only child has anything to do with his desire for more children, he replied: "No. Just Elin. She's in charge of that."
The inaugural AT&T National Golf Tournament, in which 120 players will compete for $6 million in prize money, will raise money for the Tiger Woods Foundation and the Tiger Woods Learning Center in Anaheim, Calif.