Pissing us off is O.K. with them if they can thereby impell a backlash against Muslims, or a gratuitous attack on an Islamic government that would start the global warfare and nihilistic destruction they lust for in their black hearts. They've tried to do the same thing with Israel. Of course the jihadi terrs would love it if they could trigger an complete collapse of Israel (and a subsequent genocidal, jew-killing blood bath) but short of that they have been more realistically hoping for a massively disproportionate and destructive counter-attack by Israel that would lead to U.N. intervention. (U.N. forces would be effective in restraining Iraeli security measures, but would not be able to stop Pallie terror attacks, and the attrition campaing would therefore shift favorably toward the Pallie terrs.)
Unfortunately for the evil doers they are up against opponents whose leadership is smarter than they are and (despite the adolescent nuke-mecca bravado from FR troglodites) more cool headed. Israel has had to deal with a campaign of attrition warfare horrifyingly directed against hearth and home, children and mothers, but they are fighting back hard and smart. They will eventually wear the jihadis down, or failing that will have the big wall built in another year or so. At that point their civilian population will be more defensible. If the Pallies do not stand down and negotiate peacefully by this point, The Israelis threaten a unilateral settelement of the land issue under which the Pallies will get something, but less than could have been had by negotiation. At this point the terrs may even lose their popular support among the Pallies. If not then both terrs and Pallies can go pound their (small patch of) sand.
From the American side Bush will continue patiently chipping away at terror supporting nations, keeping focus, one or two states at a time, maintaining the current multifaceted global anti-terror ops, and creatively exploiting every opportunity and opening as they arise, never pushing to the point of giving the jihadis their global armaggedon.
So, yes, in sum, you are correct. The jihadis' efforts, whether to frighten us or to piss us off, are counter productive, but only because we are smarter and saner than they are. Absolutists, nihilist, utopians, puritanical radicals simply do not have access to the resources of creativity, critical analysis and self-correction, and moral fortitude that free and civilized people do. They will always lose in the end.