1. Try to relax :) Your anxiety about the essays may be preventing you from tapping into your store of ideas!
2. I'd recommend doing a few essays without giving yourself a time constraint—if it takes you two hours, then so be it. Give yourself as much time as you need to brainstorm, plan the structure of your essay, write it out, and give it quick proofread. Once you've done this a few times and feel comfortable with the process, then start timing yourself so you can get used to a quicker version of this process when you're under pressure. Do several timed essays in this way, so that on the day of the exam, you're completely familiar with the approach of writing these essays, and it feels like just another practice essay you wrote at home.
3. Coming up with examples on the spot is definitely hard to do! What I like to do to combat this is have several topics on hand. By this, I mean that you should do a general brainstorm to come up with several topics you can easily write about—topics that you are an "expert" on, if you will.
For example, I love history. So, before test day I'd make a list of several important historical figures, events, documents, etc, and have these examples in my arsenal. Isaac Newton- inventive! Julia Child- a pioneering woman! The Emancipation Proclamation- groundbreaking! Now, of course I would think more about the influence these people/things had on the world, and of course consider how they fit into the context of questions I may be asked on the exam. But, just knowing that I can immediately recall several examples will ease my nerves, and this will likely also lead me to remember other facts that I can use as examples (I remember why Julia Child is important, and then I remember the era in which she rose to fame, and then I think about the 1960s and the events that happened in this decade, and then I think about women's rights, and so on and so forth). These first examples will work almost like a memory catalyst, and pretty soon I'll have a whole web of examples to use.
So, what interests you most? I'd recommend thinking up examples that have to do with history, gov, society, technology, education, law, and topics along these lines. Pick a few, do some brainstorming, and you'll have several examples at the ready.
I'll leave you with two resources from our blog that will help you brainstorm.