You probably don't need to worry about a back-up while you're pregnant and I believe the follow-up test is usually within a few months (I've read that it is a certain number of ejaculations at least before they're all "out"), and by then you might be in the clear without needing to use condoms.
That said, vasectomies are not 100% effective, but are very effective. They might do procedures differently now, but I know plenty of people who were born several years after mom or dad had a tubal ligation or vasectomy (not to scare you, but just get all the information you need ahead of time). I think we are planning on my husband having one whenever we are really through having kids, but I will probably stay on birth control pills as well just for hormone regulation, so we will be doubling-up but not relying on pills.