Too many goals at once?

ok, let's see here...

My understanding is that runners tend to lose muscle, and losing weight often means losing muscle mass first (hence why many body builders bulk up and then cut).

Not true. At least it's not that cut and dry.

Runners on significant calorie deficits with low protein intake and little or no strength training will have a greater tendency to lose muscle.

Losing weight CAN mean losing meaningful muscle, but it's not automatically a given.

For diet as a runner, I understand that you need to eat a more specific diet with more calories in order to support what you are doing, and to build muscle you need more protein.... but to lose weight i need to cut calories....

Sort of, but I think you are over thinking things. Elite runners with very high goals need specific diets. The rest of us can run perfectly well on most any *reasonable* diet.

Yes, you need sufficient protein to build muscle. But you also need sufficient total calories and significant resistance/strength training. Yes, that does conflict with weight loss.




Now, to your questions specifically...

Is it physically possible to train for a half marathon, do strengthening/muscle building AND cut calories all at the same time?

Yes. Lots of people run and lift while on a calorie deficit. The problem will be the whole losing weight while building muscle mass thing. That will be much harder to do. You can certainly get stronger while losing weight, but it's hard to lose weight and gain mass (since more mass = more weight).

If so, does it mean I do strength training on the same days I'm running?

No. You'll want to give 100% to each workout, so do them on different days. Or at the very least, do one in the morning and one in the evening. Doing 1 immediately after the other will slow your progress. There are ways to structure back to back workouts to maintain high intensity, but generally speaking you'll be better served doing them on different days.

I run 4-6 days a week (my long runs are Sundays), do spin 2-3 days a week, and would like to be doing strength training 3 days a week. Apparently to be on track for my weight loss goals I need to also cap my intake at 1200 calories...

How do I do it all? Is it okay to never technically have a "rest" day?

IMO, this is overkill.

First, change your mentality. Use your diet to control your weight, use exercise for everything else (health benefits, get stronger, faster, change how you look, etc).

Next, be more focused with your workouts. You have exceptionally high goals, so everything you do should be specific to those goals. A) stop spinning - it does nothing to help you progress in any of your goals. cut back the running to 3ish days a week - 2 long runs and 1 speed/hill workout. C) do 2 days of strength training. As much as possible, focus on heavy weight, low rep compound lifts. If you're brand new to lifting, starting strength is probably a good place to start. If not, I'd jump into starting strength. D) Give yourself 1 solid rest day per week. E) Make sure you are eating enough (1200 cals probably isn't going to cut it long term) AND make sure you are sleeping enough.

I forgot to mention this...

When you have competing goals, it's very possible to work on all of them at once. But, IME (I have very similar goals as you), the biggest challenge is mental, as progress will be EXCEPTIONALLY slow. Progress in any one area is normally pretty slow, but when you add other competing goals into the conversation, progress slows even further. So mentally it can be very difficult to bust your *kitten* every day and see nothing for weeks on end.