It would be a lot easier if you hadn't officially accepted the first offer. <img src="/forums/images/graemlins/lol.gif" alt="" /> But since you haven't started yet, and you're not under contract...
We had a guy at my previous job who started with us, worked for a week, and then quit to take a higher paying job elsewhere. Boss made sure his references heard about that one. Now that's burning bridges. <img src="/forums/images/graemlins/shiner.gif" alt="" />
As for job security, it sounds like you're a pretty employable guy. I myself feel pretty secure right now, but I also believe we are headed for the most prolonged downturn in the economy since 1929. Wifey and I are looking at buying a house, but before we commit to 30 years of debt, I'm going to have a real long talk with my boss about what's likely to happen to our budget in a situation like that.
The good news about NDAs is that if it's important enough to the company, they are often willing to give a bit of a golden parachute in the event you are let go. That compensation should be commensurate with the time period covered by the NDA, such as a percentage of your salary for 6, 12, 18 months, however long the NDA is in effect. That is definitely a point to negotiate. For example, my dad once lost his job when the company was bought out, but he kept getting 100% of his salary for 18 months (tied to non-disclosure/non-compete). He took a short vacation, found another job that didn't violate the agreement, and was effectively collecting two paychecks for over 12 months.
Hope your interview went well! <img src="/forums/images/graemlins/kewl.gif" alt="" />