Dear Would-Be Job-Hunter,
Looking for a new job when you have very little time is tough. Without question, looking for a job is a job.
Start by being introspective. Evaluate how badly you want to make a change. Although I completely believe your current job probably takes up most of your waking hours, many people amaze themselves (and others) when they manage to fit in time for yet another project, in addition to their already very busy lives.
Any critical life change must be discussed with your spouse. You need to clue your partner in on what you're thinking and feeling about your current job and ideas for the future. Together you need to think about how this job search and subsequent change will effect each of you and your family. Without question,you will need your spouse's support. Next, it may or may not be necessary to discuss this with your family, depending on the age of your children and their capacity for confidentiality. While investing time in your job search, you may need to bow out of some (NOT ALL) family togetherness. For sure you will need your family's support and understanding, however, if you have little ones, it may not be appropriate to have a full-scale discussion at the onset.
In addition, I suggest you think about possibly dropping other commitments and extracurricular activities during this time period. Get up earlier, and/or go to sleep later. If your current job doesn't require lunch meetings every day, schedule networking and other job-search related meetings and tasks during lunchtime as well. You may also consider working with a recruiter as part of your plan. And if you're fortunate enough to have vacation time coming up, you might decide to use that opportunity to work on your search full-time.
At the end of each day, my hope is that you can jot down at least one thing you did toward your job search, however slight some steps might seem.