"The President shall set aside and proclaim a suitable day each year, other than a Sunday, as a National Day of Prayer, on which the people of the United States may turn to God in prayer and meditation at churches, in groups, and as individuals."
Since then, it has gone back and forth, most recently last April, when US District Judge Barbara Crabb determined, in the case of the FFRF vv. President Obama and Press Secretary Gibbs (though the suit began back in 2008, and the original defendants were GWB and Dana Perino), that such a practice by the president violates the establishment clause of the Constitution's First Amendment.
In her ruling, Judge Crabb said:
So, what do the OCers think? Does the letter of the law Truman signed in violate the First Ammendment?[The National Day of Prayer] serves no purpose but to encourage a religious exercise, making it difficult for a reasonable observer to see the statute as anything other than a religious endorsement. [...] It bears emphasizing that a conclusion that the establishment clause prohibits the government from endorsing a religious exercise is not a judgment on the value of prayer or the millions of Americans who believe in its power. No one can doubt the important role that prayer plays in the spiritual life of a believer ... However, recognizing the importance of prayer to many people does not mean that the government may enact a statute in support of it, any more than the government may encourage citizens to fast during the month of Ramadan, attend a synagogue, purify themselves in a sweat lodge or practice rune magic.
For more info on the case: http://www.wiwd.uscourts.gov/assets/pdf/FFRF_v_Obama_Order.pdf