If you treat sweeping like a job, organize yourself well, and spend eight hours a day entering as many sweeps as you can, you will certainly win a lot of prizes - quite possibly enough to make a living.
Do I recommend trying to make a living entering sweepstakes? No, absolutely not. I believe that sweepstakes entry is generally too unreliable to stake your livelihood, and that of your family, on your wins. Sometimes, no matter how much or how well you enter, you just don't win. Nothing is guaranteed with sweepstakes entry.
Sweepstakes can certainly save you money. You can win a lot of great stuff that you can enjoy yourself, give away for presents, sell, or donate to charity to help offset your taxes. It's great to not have to shell out your hard-earned cash for t-shirts, fancy beauty products, getaways, and games. It's a great feeling to be able to give your friends and loved ones presents that you otherwise might not be able to afford. But saving money isn't the same as earning money, and pure cash wins, or big wins that you can leverage into a lot of cash, can be few and far between.
Also, I think that trying to make a living with sweepstakes puts a lot of pressure on what should be a fun hobby. If your entire way of living depends on a big win, you're going to spend a lot of time being disappointed - and probably eating ramen noodles.
In short, I believe that sweeping is a great hobby, and should be a source of fun and excitement. To me, having a prize show up on my front door is like Christmas in July (or April, or October). I think that there are a lot of reasons for entering sweepstakes other than just the prizes. However, making a living entering sweepstakes is just too risky for me to be able to recommend it. Enter sweepstakes as a hobby, in your spare time or while relaxing at your computer, and enjoy the rewards without putting your family's well-being on the line.