This is wrong and a bad idea. Here's why:
The recent highly acclaimed movie 'Lincoln' has a historical conflict dramatized with the Copperhead and New York Democrat Congressman Fernando Wood making the following argument against the 13th Amendment President Lincoln was spearheading:
"Congress must never declare equal those whom God created unequal."
"The Almighty has fixed the distinction of the races; the Almighty has made the black man inferior, and, sir, by no legislation, by no military power, can you wipe out this distinction."
Our history is replete with individuals that have used the authority they felt their interpretation of religious doctrine gave them to implement public policy.
Thousands of years ago, Aristotle noted that there are three basic forms of argument: Pathos, Ethos and Logos; or arguing from emotion, authority and logic. Starting a public meeting with an invocation gives the religious doctrine referred to in the prayer the imprimatur/authority that it will be used in the public policy debates/discussions held within the meeting.
Some may counter that many public deliberative bodies in the U.S. hold similar historical practices; including both bodies of Congress. Though one can appreciate the role customs have in public meetings, that would be an argument using emotion and authority instead of logic to justify the practice.
Freedom has to be protected by a governing process that is itself protected from the Fernando Woods of the world; individuals that would use the authority of the 'Word of God' to justify their actions. The tragedies our nation suffered during 9/11 and the young school girl, Malala Yousufzai, shot in Pakistan recently because she advocated educating girls should remind us that Congressman Wood, metaphorically, lives on.
Update (08/27/2013): A modern-day, extreme example of the use of ethos (authority) some feel emboldened with when they interpret religious doctrine:
Sentenced to death for a sip of water: As her religion faces persecution across the Middle East, a Christian woman explains why she faces hanging in Pakistan for the crime of ‘blasphemy’