This policy would hurt many people. Citizens would no longer be able to be visited by Muslim relatives/friends/etc who live in other countries. They may not even be able to leave the country. And they would be further tormented in their daily lives thanks to a policy that legitimizes bigotry in the minds of many.
Companies would no longer be able to send Muslim employees for business and may choose to no sever ties with the American economy - some may not even have options of non-Muslims to send and may not even have a choice.
Countries, especially those on the visitor visa waiver list (
http://travel.state.gov/content/visas/en/visit/visa-waiver-program.html) will see this as an act of discrimination against their Mulsim citizens. There would almost certainly be worsening foreign diplomatic relationships and it could result in actions against the US like embargoes.
The oppressed and impoverished will have no means of seeking sanctuary in this country if they are Muslim. This includes members of minority sects that are persecuted by members of majority sects. It also inevitably includes people who aren't Muslim but are mistaken for it because of how they look or ignorance of their beliefs.
When a big chunk of people's lives deteriorate everyone suffers. We lose contribution and coherence in society and we gain unrest that contributes to more social issues. And the basic violation of freedom of speech would surely erode the trust people have in the government and increase overall unhappiness and political dissent, and probably increase the frequency of violent reactionary demonstrations. The image of America would be greatly worsened in the eyes of the rest of the world and many valuable people would no longer want to have anything to do us either out of solidarity for Muslims or fear of ending up persecuted themselves. Inevitably some current citizens (both Muslims and non-Muslims) would denounce their citizenship and leave for the same reasons.