"She has meant the world to Barack Obama. She has poured everything she had into raising him and making him into the person that he is today," Gibbs said. "He just feels it's tremendously important that he get down there and spend time with her, as she's very sick."
The campaign of Sen. John McCain, his Republican rival, expressed sympathy for Obama.
"It's easy to forget that these are families running for president," McCain spokeswoman Nicole Wallace told "GMA." "Everyone's thoughts and prayers are with them. Certainly, Sen. McCain has Sen. Obama and his grandmother in his thoughts."
Obama's visit will probably do little to help or hurt McCain, Clarke said.
"This will make a neutral impact on the McCain campaign," she said.
"What counts here is not whether Barack Obama is out of the media spotlight for a day or two, what counts is what he is spending on paid media. He is outspending McCain by two or three times on advertising in the battleground states," she said.
Obama will attend a newly scheduled event Thursday morning in Indianapolis, Ind., after which Obama will fly to Honolulu. He will remain in Hawaii Thursday and most of Friday with his grandmother in her apartment in Oahu, the same building where he lived while attending high school nearby.
Obama's wife and daughters will not be joining him on this trip. Instead, his wife will be taking his place on the campaign trail, holding events solo in Akron and Columbus, Ohio, Friday.
Gibbs said that the campaign would continue in Obama's absence. Obama will resume his campaign in a Western swing state Saturday.