@JLeslie You’re right that most Muslim Americans do not support the violence that is associated with Islam. However the numbers are still frightening. According to Pew Research, 2011, there are approximately 1.8 million Muslims in the US. Of these, only 81% are prepared to say that violence targeting civilians should never be used to “defend Islam”. 13% said that violence against civilians is either “often”, “sometimes”, or “rarely” justified. The remaining 6% “don’t know”. That doesn’t sound like much, but that still means that there are still 234,000 Islamic extremists living in the United States, and another 108,000 who are conflicted on the issue. And, as you pointed out, Muslim Americans are some of the most moderate in the world.
Additionally, the same survey found that 2% of Muslim Americans are very favourable of Al Qaeda, and a further 3% are somewhat favourable. That makes 90,000 people residing in the United States that, while they may not carry out acts of terrorism, support one of the most notorious terrorist organisations in the world. These are ripe for recruiting, or may lend financial support to sworn enemies of the culture they are living in. 90,000 really isn’t many as a proportion, but the asymmetric nature of terrorism means it only takes a handful to create enormous problems.
I’d say those numbers are enough to support the conclusion that there is a problem with Islam.