In the AP interview, Obama was asked when he would start looking for a running mate.
"The day after I have gotten that last delegate needed to officially claim the nomination, I'll start thinking about vice presidential nominees. I think it's likely to come this week," he said. "It's a very important decision, and it's one where I'm going to have to take some time."
Robert Gibbs, a top Obama aide, said late Monday the seemingly endless Democratic contest could be resolved "in the next 24 to 48 hours."
"You're going to have a lot of superdelegates come out," he said.
Clinton left South Dakota for New York late Monday, the final leg of a whirlwind four days that took her from New York to Puerto Rico, to South Dakota and back. For a campaign pushing against long odds, it was a show of determination.
The former first lady, suffering from a recurrent cough, had to cede the microphone to her daughter twice during the day as she struggled to recover her voice. Chelsea promptly took the opportunity - to discuss health care.
Meanwhile, Obama's aides prodded uncommitted lawmakers and other superdelegates to climb aboard quickly - as Clinton struggled to hold back the fast-rising tide.
Democratic officials said that if Obama failed to gain the needed 2,118 delegates by Tuesday night, one possibility under discussion was for Senate Majority Leader Harry Reid and Speaker Nancy Pelosi to issue a statement on Wednesday urging superdelegates to state their preferences as soon as possible.