I have found 30 minutes, 6 days a week, to either run or bike for 5 years. I probably miss ~5 days a year on it, where I have to skip a few days in a row. I have two kids under 3 as well. It's not easy. I have to wake up early (5am) even on the weekends, but that's the time I can control while the kids sleep.
Eh, I believe it. 45 minutes a day doesn't count the trip to/from the gym, post-workout shower, changing, etc., and really, the people I know that actually get results from going to the gym end up spending way longer than 45 minutes there. 2-3 hours isn't unheard of. I only really say any of this because I feel like every fitness-related internet post has been along the lines of "no more excuses; if I can do it, then anyone can," which apparently isn't working.
My workouts are recently down to 30-40 minutes. Even less on a fasting day :). I have an advantage that the company has a gym, though, so there's no extra trip. My workouts are a combination of weight exercises (big 3: squat, bench press, deadlift + occasional cleans), bodyweight exercises (mostly along the lines of "Convict conditioning" books 1 and 2, and some stretching. Today, for example, in about 40 min I did (plus some stretching)
Barbell Squats 3 sets of 5
Pull-ups 3 sets of 9
Stand-to stand bridge 3 sets of 2
A static exercise on abs - 2x60s
The "secret" is that I move between exercises and sets with very little rest, I.e. do squats, then do pull ups, then back to squats - while the leg muscles get some rest, the back and arms do the work and vice versa. Of course, you need some aerobic fitness for that so you don't run out of breath. I know 2-3 hours are not unheard of, but, unless one plans to compete as a bodybuilder, diminishing returns kick in pretty fast. Even worse, one can overtrain and extra time will be very counterproductive in this case.
Of course, if you are, for example, a competitive powerlifter (I did that for a few years), you should train in a very different way - i.e. only do one exercise at a time, and have longer breaks between set etc., but if your goal is primarily health you may be way more flexible in your approach.
Another example - once a week I run home from work. It's 10 km, so takes about an hour. However, a bus takes at least 40 min, sometimes a bit more. So - I spend only 20 extra minutes, but I get a full hour of exercise! There are always ways to optimise.
'Unobtainable' is probably the wrong word for it. Most people, even those who set out to will not do it long term. That includes me and it's true. But calling it unobtainable makes it seem like it is outside an individual's control which it is not.
IMO, it is probably not more difficult (or obtainable) for most than following a good dietary regime long term.
