we have that set up too. I'm banking hours like crazy, which is great, as I'll get loads of extra holiday or early finishes.... If I can ever take them :-S
I wrote my last post at an ungodly hour here, hence its brevity, but it all stands.
If you haven't already, from this minute, you must, must, must start keeping records, and writing things down. Anything you need an action on, whether it be support, help prioritisation, work delivered by x date for delivery on y, has to be documented, and the other party knowing about it, so probably a brief email exchange. You have to be able to demonstrate you are trying hard.
I do suggest you do a time/management study for yourself. You can easily do it from a sheet of A4 paper, with lines and columns. Lines of actions, and columns recoding how long. A spreadie is better, but it has to be something you can update in moments, so that it doesn't become another (perceived) big piece of work. Miss all very well a ting you can do that from your Outlook Calendar, but just doesn't cover everything. For instance, you may have a 1 hour meeting in your calendar, but that doesn't include any preparation, or time away from your desk, getting to or from the meeting. If you have to drag some papers together, or print a slide stack, it might only be 5 minutes, but coupled with allowing 5 minutes each end of the meeting Toget to and from meeting rooms on other floors, you have 15. Minutes, or an hour, if you have 4 such meetings in a day. Similarly, with phone calls. Log each one made or taken, and it's duration. You can time them on your phone, probably.
It's utterly terrifying how it all adds up. Sometimes it's terrifying how it doesn't add up too!!
Armed with that you have solid evidence for discussing with your boss and/or HR. Not a conversation about being "rushed off your feet". With that evidence, it's easy to ask your boss which stuff you are not to do, or what protective actions you can take. Protective actions could be not touching email or the phone one day a week, to allow quiet concentration, or working from home one day a week. It's amazing how much time is spent with shoulder surfers who just turn up and steal 15 valuable minutes.
The ball is in your court. It sounds like your boss has dropped a bit of a brick and it might be a tough issue for him to solve if he has losbudget, but by doing the foregoing you are proving your points AND providing HIM with evidence to back up support for you.
You need to get your head organised over this one, and be strong.