Is it possible? Anything is possible. The correct question you should be asking is, is it wise? I'm going to play devil's advocate here (since you already have many successful supermom homeschooler viewpoints) and point out a few confounding factors. There are 168 hours in a week. You presumably sleep 8 hours a night (56 hours), so after sleeping you have 112 hours in your week.
168 - 56 = 112 hours.
Let's assume you work a typical 40 hour workweek with a typical 1/2 hour commute on each end of 5 days (.5 hr x 2x/day x 5 workdays).
112 - 45 = 67 hours.
While you're working, your kids need to be someplace safe, either daycare, or bartering with a relative or neighbor (for which you'll owe either money or a fair energy exchange of something you have to offer in return). Most parents, if they were rolling in dough from a well-paying job, would either move to a better school district or enroll their children in private school, not homeschool, so I'm going to make a presumption here that you'll be working for a more modest salary and will either be paying a daycare bill while your kids are in school (average cost in before-tax dollars $15,000/yr/child) or bartering your services/trading favors. Therefore, for every hour you are at work and commuting to/from work (45 hours) you are going to own an additional amount of your life's energy EQUAL to those 45 hours to somebody else.
67 - 45 child care exchange = 22 hours.
When you get home from work every night, your kids are going to be hungry and you'll need to cook supper, sit down, eat with your kids, then clean up the dishes afterwards. Let's presume you're going to feed your kids a 40 minute box of hamburger helper every night and rush through the meal. Even if you save cleanup until after they go to bed, you still need to do that, so that's at minimum 1 hour per day x 7 days. You'll also need to feed them breakfast before you go to work, pack their lunches for wherever they are to go (or set food aside for the babysitter), get them dressed, and other morning tasks which will take, at minimum, another hour per day. Two hours lost per day, plus two extra hours on the weekend because I assume you, not the babysitter, will be feeding them lunch.
22 hours - 16 hours = 6 hours.
Now, every night your kids will need help with their bedtime routine to get on their PJ's, brush their teeth, take a bath, get tucked into bed, pick up their toys, read a bedtime story, etc. In our house, this routine takes an hour or more x 7 days per week.
6 - 7 bedtime routine = -1 hour
Now, if you're like most people, you need to eat, so at least one day per week you're going to have to make a trek to the grocery store and buy food. Since you'll be working, this will most likely be during a very busy time of the day, so it will take at least 2 hours (more likely 3).
-1 - 2 = -3 hours
To meet your minimum state education requirements for a homeschool education plan, they're going to demand you can demonstrate you're willing to put in AT LEAST as many hours as schools are required to dedicate to educating your child (6 hours per day). Many homeschool moms are flexible about -when- they squeeze in the education opportunities for their kids to be at various times of the day, but the fact remains that to teach your child, you need to be able to dedicate a certain number of hours to "feeding the sponge" and kids learn best when things are on somewhat of a consistent schedule (though that scheduled doesn't need to be from 9-3 every day)
-3 - 30 ed time = -33 hours
As you can see, the math simply doesn't add up. You're already 33 hours per week in the hole and you don't have a single second available to do laundry, clean the house, make love to your husband, or go to church. If you pay a daycare bill instead of swapping favors, once you pay taxes (including taxes on any portion of the income used to pay the childcare bill over and above the $5200 limit) and gas to commute to work you're probably going to be in the hole or just be breaking even. That's why so many homeschooler supermoms are also dedicated stay-at-home moms who peruse this website to glean ways to make ends meet on one income. You -COULD- eliminate that 45-hour daycare-energy drain by swapping off shifts with your husband so that one of you is home with the kids during the day while the other works, but I guarantee within 2 years one of you will be speaking to a divorce attorney because split-shift marriages become failed marriages within a very short period of time.
Perhaps some of the super homeschool moms could either suggest ways Pumpkin can afford to stay home with Lil'Pumpkin to homeschool, or enrich Lil'Pumpkins inadequate public school curriculum with supplemental homeschooling once she returns to work?