From the State Department website:
A U.S. citizen may acquire foreign citizenship by marriage, or a person naturalized as a U.S. citizen may not lose the citizenship of the country of birth.U.S. law does not mention dual nationality or require a person to choose one citizenship or another. Also, a person who is automatically granted another citizenship does not risk losing U.S. citizenship. However, a person who acquires a foreign citizenship by applying for it may lose U.S. citizenship. In order to lose U.S. citizenship, the law requires that the person must apply for the foreign citizenship voluntarily, by free choice, and with the intention to give up U.S. citizenship.
http://travel.state.gov/travel/cis_pa_tw/cis/cis_1753.html
I am a dual citizen (actually, a citizen of three countries) and am fully in compliance with US law.
You can be a dual citizen and your children can be, but I don’t think they can be President.
If Obama is a dual citizen, he has done nothing wrong with regards to that. He is entitled to it, but can he be President. That is the question.