There are 6 of us.....so I'm on the fence about getting them for our 2014 cruise as well. I may get them in batches......DH/Me, 2 Daughters and then get our 2 sons done. That way I don't pay for them all at once.
Do you need your Social Security card at all to obtain a Passport? We have certified birth certificates for our children, but the youngest 3 are adopted and their original SS cards do NOT match their birth certificates. I have been procrastinating in getting those changed....guess I need to get on the ball before they are grown LOL.
Buying in batches is nice. Check out the ages of the kids, so that you can get as close to perfect timing as possible. For instance, if one child gets a passport at 1, they'll get another at 6, then another at 11, and then 5 years later they are 16 and that is perfect timing b/c then they get the adult passport which is good for 10 years.
If you have a 3 year old, though, the first is at 3, next at 8, next at 13, and I'm not actually sure if a child's passport can be good beyond 16. So they might have to just get the adult passport while the child passport still has time left on it. That's not perfect timing. So work out the batches so you're not causing imperfect timing.
We just have one (sniffle) and managed to fall into perfect timing.
The passport website is actually quite nice and has lots of info.

First timers look
here.
Primary Evidence of U.S. Citizenship (One of the following):
Previously issued, undamaged U.S. Passport
Certified birth certificate issued by the city, county or state*
check box Consular Report of Birth Abroad or Certification of Birth
Naturalization Certificate
Certificate of Citizenship
Primary Identification (One of the following):
check box Previously issued, undamaged U.S. passport
check box Naturalization Certificate
check box Valid Driver's License
check box Current Government ID (city, state or federal)
check box Current Military ID (military and dependents)
No SS
cards needed. But the application, form DS-11, does require the SS *number*.
Take some nice, quiet time to really look at the website. They have a LOT of info, and they have all sorts of "but what if THIS is my situation" contingencies covered. This isn't relevant for you I believe, but they have a whole flowchart of various situations where you can't have both parents there in person to get the kiddies their first passport. It's a good site. And when I've called for more info, they have been extremely pleasant and helpful.
We have
trip insurance, how does that factor in? Just curious as this is our first cruise
They said "How you answer this question will tell you what amount of risk you are willing to accept.", and I think that's the explanation. If you're nervous about something going wrong and buy the insurance because of the nervousness, then you worry enough about something going wrong that you want to be prepared with passports.
I personally would rather pay now for the passports instead of budget the money anyway, plus extra, to get them expedited if something happens. DH had to expedite his passport because his had expired and he needed a new one "yesterday:* for a job that required travel, and it was NOT a pretty price. And that's just for one. With the joy of a new job behind it, not "will we be OK?" as the background emotion.
And, of course, we always have the "win a round-the-world trip" in our minds. Gotta be ready for that possibility!
*not actually yesterday...this was back in '09, LOL. which feels like yesterday, but is not. and then let's not talk about when he put his year-old passport through the wash , thereby destroying it, causing ANOTHER to have to be expedited.