Ah, so Buddhism wasn't left out, after all!
Lama Surya Das passed on this fascinating bit. Richard Blum, who is the husband of California Senator Diane Feinstein, also happens to be a major supporter of Buddhism. He was up on the platform during the swearing in.
Beforehand, he told Barack Obama that he had with him a white khata -- a silk Tibetan scarf -- given him by His Holiness the Dalai Lama. Blum described what happened next in a letter to an associate of the Dalai Lama:
"I offered it to President Obama before the ceremony. I said that I could get it delivered to him later. He said, no, that he was going to take it and have it with him; in fact, it was in his pocket when he was sworn-in."
What's the significance? Lama Surya Das, one of the nation's leading Buddhist monks/teachers, explains: