The growing secular community in the US now makes up nearly one-fifth of the population and one-third of the population under the age of 30. Even with its fast growth, non-believers are still ridiculed in the mass media and are America' most distrusted minority (http://www1.umn.edu/news/news-releases/2006/UR_RELEASE_MIG_2816.html).
Furthermore, after Pastor Giglio's removal from the ceremony, it makes no sense for the President to put his hand on a book that has passages that he has publicly disapproved of (the same passages Giglio draws his anti-LGBT sermons from).
We believe it would be more meaningful for the Pres. to place his hands on the U.S. Constitution, or his immediate family's shoulders. This would also be an enormous sign of solidarity with the outspoken secular community.