"I've made the selection, that's all you're gonna get," Obama said told reporters while campaigning in Virginia Thursday.
Obama didn't say whether he's informed his pick yet.
In an exclusive interview, Early Show co-anchor Harry Smith asked Obama, "In the final analysis, did you find it more intellectual, or was it a gut check?"
"I think it's a combination of things," Obama said. "I think you've got to, obviously, feel comfortable with the person."
Obama is planning to announce his choice in a text message to supporters sometime before Saturday afternoon, when he's scheduled to appear with his pick in Illinois.
Asked by an Associated Press reporter when the text would be sent, Obama just grinned and said, "Wouldn't you like to know?"
Earlier on Thursday, Obama met with Virginia Gov. Tim Kaine at a hotel in Richmond, reports CBS News' Maria Gavrilovic.
At a town hall meeting in Richmond later in the day, Obama was introduced by Kaine, who is widely believed to be on the short list of possible vice presidential contenders.
Kaine batted away questions about his prospects.
"I'm going to let the campaign speak for the campaign," he said.