You make a good point. It seems that the First Amendment will be a serious handicap in America's battle against terrorism. But we should not weaken the First Amendment; rather, we should withdraw its protections from Islam, which abuses them.
Suppose a Constitutional amendment along the following lines:
"For all purposes under this Constitution, and the laws and treaties of the United States, Islam shall not be considered a religion; and the practice of Islam in any of its forms may be proscribed by the enactment of general laws as the Congress may deem advisable, or by executive order signed by the President."
Of course, such an amendment would have no chance of passing right now. But suppose that Freepers laid the groundwork in advance, and then immediately after the next muslim atrocity on American soil, execute a plan to have that Amendment proposed and pushed and ratified?