You don't have to be in good enough shape to go backpacking.
I agree wholeheartedly with lori.
Walking is probably the best way to prepare yourself. You can add a pack and some weight after a bit to get a feel for what you're up against, but you don't need to carry it for miles at full weight when prepping for a hike.
Start by walking a mile or two, more if you're ready for it. Do that two or three times a week for a couple weeks and you'll already see an increase in your stamina. At that point you're ready to hike.
Plan a simple trip that takes you about as far in as your daily hikes, just take as many breaks as you want on the way in. Stop for snacks and water, and rest too. Once you found or arrived at your spot, spend a night or two, and then hike back out.
Assess your experience, ability, and your gear when you get back and then start planning your next trip.
If you have the time to get out often you'll be amazed at how fast you can increase your endurance. You don't even need to "Push Yourself" to do this. It comes without that, so don't. You're most always in a perfect spot to stop and enjoy the scenery if you want to, so you have the perfect excuse to stop anyway.
Hiking is, at most, and best, only half of backpacking. The rest is being somewhere.
Bill