I think the idea of “not having time” for working out really doesn’t make a whole lot of sense. Yes, when you have a busy schedule, it seems like getting 45-60 minutes a day can be rough, and it certainly is when you start, but once you get past the start, it is largely time neutral.
Consider, being out of shape generally means you need a little bit more sleep than when you’re in shape. Also consider that being in shape, particularly if you do some exercise in the morning, can improve focus and, thus, make you more productive in the time you have. Thus, I think the time you spend exercise ultimately ends up more or less paying for itself.
Personally, I work out a bit more than that, I don’t do it every day, since I like having at least one day a week for recovery, but I also do more weight training, so I end up doing ~11 hours or so a week. I do generally make two trips though, I do some cardio and stretching in the morning and weight training in the evening, but that’s mostly because I just don’t want to get up early enough to do everything in the morning and I have cardio equipment at my apartment complex which I use in the morning, so I only have to make a trip to the gym for weight training.
If you’re having trouble making time for it, just try waking up earlier and doing it in the morning. You get added benefit of it helping you wake up and of having a somewhat raised metabolism throughout the day, so it helps with energy and potentially losing weight.