FUD works because people don't think things through; we are very bad at proper risk assessment. The question remains whether we should trust our government to do better - or suspect it of abusing the opportunity this allegation makes. Recent history encourages the latter!
Keep in mind that it's quite literally the government's job to try to protect against or prepare for worst case scenarios. FEMA does it with natural disasters. The military plays end-of-the-world wargames and trains for battle against people we hope never to fight against. And of course, the various Homeland Security agencies look for people who want to do America or its citizens harm. It's their job to try to anticipate or prevent worst-case scenarios. We hire people to do this so we won't have to.
This create a quandary of sorts. On the one hand, they're by far the most qualified to answer the question as to how legitimate the potential threats are. On the flip side, it's in their own best interest to magnify the threats so as to increase their own budgets and importance, which is a natural trend for any bureaucratic agency. We can, however, blame them for overreaching their legal and constitutional bounds in carrying out their mandate. And we need to call them out when we see that they've magnified threats beyond their logical probability as well. That second part is a bit harder to do - realistically, only our elected officials have access to the most sensitive raw sources and data, so we have to trust that they'll exercise proper oversight in that regard.
As lay persons, you and I (and the general public) are not really qualified to determine whether various threats are real or not, both because a) it's not our area of expertise, and b) we don't have enough data to make a well-informed judgment. For instance, many terrorists may have been stopped by good intelligence, but it's possible this information can't be released to the public (similar to the allies Ultra/Enigma project in WWII), for fear of compromising the source or techniques used. This leaves the public feeling like there is no credible threat, which on the one hand, is a good thing, but on the other, leads people to question the necessity of the very agencies preventing the attacks. It's unfortunate that these agencies have undermined their own trust, because now we have a hard time believing them even if they're telling us the truth.
Who do you turn to when your best guard dog has been crying wolf?