Does America (and W. Europe) need to stop worrying about giving offense and declare all-out war on rad. Islam?

I mean to seriously root out, domestically, those who wish to enact fundamentalist Islamic beliefs such as Sharia Law, and who believe their religion justifies violent jihad against those they consider infidels. America and Europe may have to build 10,000 new prisons over the next 100 years. So be it.