He certainly wasn't looking for it, according to his daughter Deana Martin, and at first rebuffed NBC's advances. From the LAT:
"They called him again," his daughter recalled. "He said, 'They want to have a meeting with me.' He told all [of the family], 'When I go in tomorrow, I am going to ask them for a ridiculous amount of money so they will turn me down. I am going to tell them I don't want to rehearse, so I'm sure they will turn me down. And then I am going to tell them I only want to tape it on Sunday afternoons after 1. So for sure they won't go for it.' "He came home that night and said, 'They went for it. So now I have to do it."'
The show lasted nine seasons, with Martin playing the drunk playboy - and, true to his word, he didn't rehearse before taping.
Martin was swigging apple juice and not hard liquor in his glass when he performed. "He would be home for dinner every night," recalled his daughter. "He would come home and he and mom would have their one cocktail at the bar. They had their half-hour alone time. He was kind. He would get up early in the morning and play golf. He was so different from what everybody thought he was. There was no one who could do Dean Martin better than Dean Martin."